bluuebunny/crossref_metadata_2025 huggingface dataset:
A lambda proof of the P-W theorem
Authors: Hirokawa Sachio , Komori Yuichi , Nagayama Misao
Published: May 2006

The logical system P-W is an implicational non-commutative intuitionistic logic denned by axiom schemes B − (b → c) → (a → b) → a → c. B′ = (a → b) → (b → c) → a → c. I - a → a with the rules of modus ponens and substitution. The P-W problem is a problem asking whether α - β holds if α → β and β → α are both provable in P-W. The answer is affirmative. The first to prove this was E. P. Martin by a semantical method.

In this paper, we give the first proof of Martin's theorem based on the theory of simply typed λ-calculus. This proof is obtained as a corollary to the main theorem of this paper, shown without using Martin's Theorem, that any closed hereditary right-maximal linear (HRML) λ-term of type α → α is βη-reducible to λxx. Here the HRML λ-terms correspond, via the Curry-Howard isomorphism, to the P-W proofs in natural deduction style.
Properties of ideals on the generalized Cantor spaces
Authors: Kraszewski Jan
Published: May 2006

We define a class of productiveσ-ideals of subsets of the Cantor space 2ω and observe that both σ-ideals of meagre sets and of null sets are in this class. From every productive σ-ideal we produce a σ-ideal of subsets of the generalized Cantor space 2κ. In particular, starting from meagre sets and null sets in 2ω we obtain meagre sets and null sets in 2ω, respectively. Then we investigate additivity, covering number, uniformity and cofinality of . For example, we show that

Our results generalizes those from [5].
Dictatorship, Democracy, and Development
Authors: Olson Mancur
Published: May 2006

Under anarchy, uncoordinated competitive theft by “roving bandits” destroys the incentive to invest and produce, leaving little for either the population or the bandits. Both can be better off if a bandit sets himself up as a dictator—a “stationary bandit” who monopolizes and rationalizes theft in the form of taxes. A secure autocrat has an encompassing interest in his domain that leads him to provide a peaceful order and other public goods that increase productivity. Whenever an autocrat expects a brief tenure, it pays him to confiscate those assets whose tax yield over his tenure is less than their total value. This incentive plus the inherent uncertainty of succession in dictatorships imply that autocracies will rarely have good economic performance for more than a generation. The conditions necessary for a lasting democracy are the same necessary for the security of property and contract rights that generates economic growth.
Normative and Structural Causes of Democratic Peace, 1946–1986
Authors: Maoz Zeev , Russett Bruce
Published: May 2006

Democratic states are in general about as conflict- and war-prone as nondemocracies, but democracies have rarely clashed with one another in violent conflict. We first show that democracy, as well as other factors, accounts for the relative lack of conflict. Then we examine two explanatory models. The normative model suggests that democracies do not fight each other because norms of compromise and cooperation prevent their conflicts of interest from escalating into violent clashes. The structural model asserts that complex political mobilization processes impose institutional constraints on the leaders of two democracies confronting each other to make violent conflict unfeasible. Using different data sets of international conflict and a multiplicity of indicators, we find that (1) democracy, in and of itself, has a consistent and robust negative effect on the likelihood of conflict or escalation in a dyad; (2) both the normative and structural models are supported by the data; and (3) support for the normative model is more robust and consistent.
Lawyers, Organized Interests, and the Law of Obscenity: Agenda Setting in the Supreme Court
Authors: McGuire Kevin T. , Caldeira Gregory A.
Published: May 2006

Each year thousands of cases and litigants come to the Supreme Court. How can the Court find the most important cases to decide? The law of obscenity illustrates particularly well the Court's problem as it constructs its plenary agenda. Using data drawn from petitions for certiorari and jurisdictional statements filed with the Supreme Court from 1955 to 1987, we formulate and test a model of case selection in which professional obscenity lawyers and organized interests figure as critical elements in the process of agenda building. We also encounter strong evidence of the Court's differential treatment of several different litigants. Moreover, the calculus of selection changed markedly over time, as the Court itself changed; the Burger Court and Warren Court weighed several of the criteria quite differently.
Incentives to Cultivate Favored Minorities Under Alternative Electoral Systems
Authors: Myerson Roger B.
Published: May 2006

A simple model is used to compare, under different electoral systems, the incentives for candidates to create inequalities among otherwise homogeneous voters, by making campaign promises that favor small groups, rather than appealing equally to all voters. In this game model, each candidate generates offers for voters independently out of a distribution that is chosen by the candidate, subject only to the constraints that offers must be nonnegative and have mean 1. Symmetric equilibria with sincere voting are analyzed for two-candidate elections and for multicandidate elections under rank-scoring rules, approval voting, and single transferable vote. Voting rules that can guarantee representation for minorities in multiseat elections generate, in this model, the most severely unequal campaign promises.
An Analysis of Congressional Career Decisions, 1947–1986
Authors: Kiewiet D. Roderick , Zeng Langche
Published: May 2006

Most previous research on congressional career decisions has focused on one of two binary choices—between retiring and running for reelection, or between running for reelection and seeking higher office. But most of the time, representatives face all three choices simultaneously. Employing a “mother logit” model, we estimate the effects of relevant variables both on pairwise comparisons (conditional probabilities) and on the unconditional probabilities of choosing each one of these three alternatives. Probably most intriguing is our finding that a member's age has little or no effect upon the unconditional probability of running for reelection. The interrelatedness of career options is seen particularly clearly in the case of incumbents who had been redistricted out of their seats. When they had an opportunity to run for higher office, they were likely to take it. Only when they lacked such an opportunity were they more likely than other members to opt for retirement.
Inequality and Political Violence Revisited
Authors: Wang T. Y. , Dixon William J. , Muller Edward N. , Seligson Mitchell A.
Published: May 2006

In their 1987 article in this Review, Muller and Seligson used logged ordinary least-squares (LOLS) to estimate the effect of income inequality on cross-national levels of deaths by political violence. T. Y. Wang challenges the robustness of the main conclusion and argues for the application of a maximum likelihood approach—the exponential Poisson regression (EPR) model—rather than LOLS. He concludes that the widely used LOLS approach yields misleading conclusions when applied to event count data. Dixon, Muller, and Seligson replicate previous work using both LOLS and EPR approaches and conclude that in most—but not all—respects the two approaches yield similar results, supporting the effect of inequality when the specifications are identical. They also argue (in response to concerns expressed by Brockett 1992) that the inequality results are robust when account is taken systematically of the best information on underreporting of deaths.
The Moral Sense
Authors: Wilson James Q.
Published: May 2006

The central problem for social science is to explain social order. How do people manage to live together? One can discern two ways of answering that question. The first view is normative and communal: people learn from their culture customs that provide an internal compass guiding them to act in ways that minimize conflict and ensure comity. The second view is rationalistic and individualistic: order is created by explicit and implicit agreements entered into by self-seeking individuals to avert the worst consequences of their predatory instincts. In the first view, order is natural and prior to any social contract or government institution; in the second, it is contrived and dependent on agreements and sanctions. Rules are obeyed in the first case because they have moral force, in the second because they convey personal advantage. In the first view, compliance is automatic and general; in the second, it is strategic and uncertain.

The normative view has been under heavy attack for several decades for at least three reasons: it seems to imply a complacent functionalism; it appears to minimize or deny the value of conflict; and it lacks the theoretical power found in the assumption that people always seek their own interests. I believe that one can grant, up to a point, all of these objections and still be left dissatisfied with the alternative, namely, that social order is contrived, based on calculation, and dependent on individual assent.
A Model of the Political Economy of the United States
Authors: Alesina Alberto , Londregan John , Rosenthal Howard
Published: May 2006

We develop and test a model of joint determination of economic growth and national election results in the United States. The formal model, which combines developments in the rational choice analysis of the behavior of economic agents and voters, leads to a system of equations in which the dependent variables are the growth rate and the vote shares in presidential and congressional elections. Our estimates support the theoretical claims that growth responds to unanticipated policy shifts and that voters use both on-year and midterm elections to balance the two parties. On the other hand, we find no support for “rational” retrospective voting. We do reconfirm, in a fully simultaneous framework, the “naive” retrospective voting literature's finding that the economy has a strong effect on presidential voting. We find congressional elections unaffected by the economy, except as transmitted by presidential coattails.
Reconstructive Democratic Theory
Authors: Dryzek John S. , Berejikian Jeffrey
Published: May 2006

While the idea of democracy has never been more universal or more popular, both democratic theory and the empirical study of democratic possibilities are in some disarray. We seek a productive reconnection of these two endeavors with democratic discourse through close attention to the language of democracy as used by ordinary people and political actors. Reconstructive inquiry determines how the individuals who are the potential constituents of any democratic order themselves conceptualize democracy and their own political roles and competences. We deploy an intensive method—Q methodology—for the study of individual characteristics, capabilities, and dispositions in combination with political discourse analysis. Four discourses are discovered in an analysis of selected U.S. subjects: contented republicanism, deferential conservatism, disaffected populism, and private liberalism. These results can be used to relate democratic theory to live possibilities in democratic discourse.
What Moves Policy Sentiment?
Authors: Durr Robert H.
Published: May 2006

In spite of the fact that political eras in the United States are widely (and often ambiguously) defined in terms of a general policy sentiment or mood, political scientists have done little in the way of rigorous analysis regarding this subject. I argue that shifts in domestic policy sentiment along a liberal–conservative continuum may be understood in part as responses to changing economic expectations. Specifically, expectations of a strong economy result in greater support for liberal domestic policies, whereas anticipation of declining economic conditions pushes the national policy mood to the right. Using quarterly data for the period 1968–88, I present a multiple-time-series error correction model that lends considerable support to the hypothesis.
Social Construction of Target Populations: Implications for Politics and Policy
Authors: Schneider Anne , Ingram Helen
Published: May 2006

We argue that the social construction of target populations is an important, albeit overlooked, political phenomenon that should take its place in the study of public policy by political scientists. The theory contends that social constructions influence the policy agenda and the selection of policy tools, as well as the rationales that legitimate policy choices. Constructions become embedded in policy as messages that are absorbed by citizens and affect their orientations and participation. The theory is important because it helps explain why some groups are advantaged more than others independently of traditional notions of political power and how policy designs reinforce or alter such advantages. An understanding of social constructions of target populations augments conventional hypotheses about the dynamics of policy change, the determination of beneficiaries and losers, the reasons for differing levels and types of participation among target groups, and the role of policy in democracy.
Expectations and Preferences in British General Elections
Authors: Nadeau Richard , Niemi Richard G. , Amato Timothy
Published: May 2006

We address two questions: How do people form their expectations about the likely winner of the next general election? and What are the links between expectations and votes? Using data collected by the Gallup organization in Great Britain, we find that the expectations formation process (1) has a significant inertia component but also a rapid adjustment to current information; (2) reflects voters' ability to translate economic expectations into political forecasts; and (3) is “time-bounded,” possessing special characteristics immediately before and after a general election. The analysis also confirms the existence of a small bandwagon effect, whereby expectations that one party will win inflate that party's vote. The ability of voters to make reasonable forecasts without being unduly influenced by their own preferences suggests that under normal circumstances voters are expressing real preferences and not simply following the crowd.
Peace, War, and the Balance of Power
Authors: Wagner R. Harrison
Published: May 2006

Every possible relation between the distribution of power and the likelihood of war has been defended somewhere in the literature on international politics: war is least likely if power is distributed equally, war is least likely if power is distributed unequally, and the distribution of power has no effect on the likelihood of war. I try to settle this dispute by examining the effect of expectations about the outcome of war on the choice between war and negotiation. I argue that each of these mutually contradictory propositions can be derived from some plausible set of premises and thus that which one is correct depends on which set of premises best describes a situation. The most important factors affecting the relation between the distribution of power and the likelihood of war are (1) whether the terms of a compromise agreement that might be accepted in lieu of war affect the distribution of power between the antagonists and therefore the probability that the agreement will be enforced and (2) how many states' interests will be affected by the outcome.
The Tower of Babel as a Coordination Game: Political Linguistics in Ghana
Authors: Laitin David D.
Published: May 2006

The problem of choosing an indigenous official language for multilingual states in general and for Ghana in particular is treated as one of coordination in an n-person tipping game. Even with an assumption that the equilibrium outcome of all-English is deficient, the mechanisms for reaching an indigenous language solution are difficult to find. A lottery (a theoretically attractive approach to the solution of coordination games) is less attractive when applied to the issue of language coordination. Empirical data based on interviews from six different regions of Ghana show the limits and possibilities of the theoretic solution. Going back to theory, a mechanism for the successful promotion of an indigenous language outcome is proposed.
Multiculturalism and the Problem of Particularism
Authors: Parens Joshua
Published: May 2006

When Kant first used the term “culture,” he referred to the human capacity to will universal moral laws. Multiculturalists object to the denial of “difference” implicit in Kantian as well as all other Enlightenment forms of universalism. Their objection stems from their more particularistic understanding of culture, which for the most part everyone shares today. Plato is frequently said to be the fount of (universal) natural law theory; yet a medieval Muslim philosopher, Alfarabi, presents a Plato who denies moral universalism but acknowledges the possibility of some form of universalism, at least in the realm of knowledge. Alfarabi's Plato thereby provides a corrective for both extreme contemporary particularism and extreme Kantian universalism.
Do Bills of Rights Matter? The Canadian Charter of Rights and Freedoms
Authors: Epp Charles R.
Published: May 2006

Although constitutional protection for rights is increasingly popular, there is little systematic research on the extent to which bills of rights affect the process of government. This article examines the effects a bill of rights may be expected to produce, and then uses a quasi-experimental design to analyze the effects of the Canadian Charter of Rights and Freedoms on the Canadian Supreme Court's agenda. The data suggest that the Charter indeed has influenced the Court's agenda, although the effects are more limited than generally recognized. More important, the data suggest that a number of the influences often attributed to the Charter likely resulted instead from the growth of what I call the support structure for legal mobilization, consisting of various resources that enable litigants to pursue rights-claims in court. The political significance of a bill of rights, then, depends on factors in civil society that are independent of constitutional structure.
Do Majority-Minority Districts Maximize Substantive Black Representation in Congress?
Authors: Cameron Charles , Epstein David , O'Halloran Sharyn
Published: May 2006

Majority-minority voting districts have been advanced as a remedy to the underrepresentation of minority interests in the political process. Yet, their efficacy in furthering the substantive goals of minority constituents has been questioned because they may dilute minority influence in surrounding areas and lead to an overall decrease in support for minority-sponsored legislation. Thus, there may be a trade-off between increasing the number of minority officeholders and enacting legislation that furthers the interests of the minority community. Using nonlinear estimation techniques, we simulate the districting strategies that maximize substantive minority representation, and find that such a trade-off does exist. We also find that, outside of the South, dividing minority voters equally across districts maximizes substantive representation; inside the South the optimal scheme creates concentrated districts on the order of 47% black voting age population. In addition, minority candidates may have a substantial chance of being elected from districts with less than 50% minority voters.
The Claim of Issue Creation on the U.S. Supreme Court
Authors: Epstein Lee , Segal Jeffrey A. , Johnson Timothy
Published: May 2006

We argue that a variant of the sua sponte doctrine, namely, the practice disfavoring the creation of issues not raised in the legal record, is a norm with substantial consequences for the U.S. Supreme Court. Without it, justices would act considerably more like legislators, who are free to engage in “issue creation,” and less like jurists, who must wait for issues to come to them. Yet, McGuire and Palmer claim that justices engage in issue creation in a “significant minority” of their cases. We dispute this finding because we think it is an artifact of the way McGuire and Palmer collected their data. Indeed, for virtually every case in which they found evidence of issue creation, we show that the issue was actually present in at least one of the litigants' briefs. This suggests that justices may be policy seekers, but they are not policy entrepreneurs; an that briefs filed by third parties (such as amici curiae) are generally not a source of important issues considered by the Court.
Issues, Agendas, and Decision Making on the Supreme Court
Authors: McGuire Kevin T. , Palmer Barbara
Published: May 2006

In the process of agenda setting, the U.S. Supreme Court is limited to selecting from among only those cases brought before it. Despite this limitation, the justices possess considerable discretion and can reshape the issues in a case as a means of advancing their policy preferences. With data drawn from the Court's opinions, we find that, over the past twenty-five years, the justices have evinced a frequent willingness to expand the issues on their plenary docket and resolve questions not formally presented by the parties. We conclude that, notwithstanding informal norms that disapprove of this practice, issue fluidity is an important component in a continuous program of agenda building.
The Effect of Dynamic and Static Choice Sets on Political Decision Making: An Analysis Using the Decision Board Platform
Authors: Mintz Alex , Geva Nehemia , Redd Steven B. , Carnes Amy
Published: May 2006

Previous studies of political decision making have used only “static” choice sets, where alternatives are “fixed” and area prioriknown to the decision maker. We assess the effect of adynamicchoice set (new alternatives appear during the decision process) on strategy selection and choice in international politics. We suggest that decision makers use a mixture of decision strategies when making decisions in a two-stage process consisting of an initial screening of available alternatives, and a selection of the best one from the subset of remaining alternatives. To test the effects of dynamic and static choice sets on the decision process we introduce a computer-based “process tracer” in a study of top-ranking officers in the U.S. Air Force. The results show that (1) national security decision makers use a mixture of strategies in arriving at a decision, and (2) strategy selection and choice are significantly influenced by the structure of the choice set (static versus dynamic).
Unequal Participation: Democracy's Unresolved Dilemma Presidential Address, American Political Science Association, 1996
Authors: Lijphart Arend
Published: May 2006

Low voter turnout is a serious democratic problem for five reasons: (1) It means unequal turnout that is systematically biased against less well-to-do citizens. (2) Unequal turnout spells unequal political influence. (3) U.S. voter turnout is especially low, but, measured as percent of voting-age population, it is also relatively low in most other countries. (4) Turnout in midterm, regional, local, and supranational elections—less salient but by no means unimportant elections—tends to be especially poor. (5) Turnout appears to be declining everywhere. The problem of inequality can be solved by institutional mechanisms that maximize turnout. One option is the combination of voter-friendly registration rules, proportional representation, infrequent elections, weekend voting, and holding less salient elections concurrently with the most important national elections. The other option, which can maximize turnout by itself, is compulsory voting. Its advantages far outweigh the normative and practical objections to it.
Legal Theory in the Collapse of Weimar: Contemporary Lessons?
Authors: Dyzenhaus David
Published: May 2006

The Weimar Republic is frequently invoked in political theory as an example when the issue is the appropriate response of liberal democracies to internal, fundamental challenges. I explore that example through the lens of a 1932 court case that tested the legality of the federal government's “coup” against Prussia. In my analysis of the court's judgment and of the arguments of three political and public law theorists, Carl Schmitt, Hans Kelsen, and Hermann Heller, I argue for Heller's democratic vision of the rule of law. In my conclusion, I compare problems in Kelsen's position with problems in the recently articulated position of John Rawls in order to suggest what lessons Weimar may have for contemporary political theory.
Stability and Coordination in Duverger's Law: A Formal Model of Preelection Polls and Strategic Voting
Authors: Fey Mark
Published: May 2006

This paper investigates the dynamics of the “wasted vote” phenomenon and Duverger's Law. I construct a theoretical model in order to consider how preelection polls serve to inform the electorate about the relative chances of the candidates and how that information acts over time to decrease the support of the trailing candidate. The results shed light on how public opinion polls can aggregate information in the electorate and coordinate voters on the viable candidates in the election. Specifically, I show that in a Bayesian game model of strategic voting there exist non-Duvergerian equilibria in which all three candidates receive votes (in the limit). These equilibria require extreme coordination, however, and any variation in beliefs leads voters away from them to one of the Duvergerian equilibria. Thus, non-Duvergerian equilibria are unstable, while two-party equilibria are not. In addition, I describe how preelection polls provide information to voters about the viability of candidates and can thus be used by voters to coordinate on a Duvergerian outcome.
The Strategic Timing of Position Taking in Congress: A Study of the North American Free Trade Agreement
Authors: Box-Steffensmeier Janet M. , Arnold Laura W. , Zorn Christopher J. W.
Published: May 2006

A critical element of decision making is the timing of choices political actors make; often when a decision is made is as critical as the decision itself. We posit a dynamic model of strategic position announcement based on signaling theories of legislative politics. We suggest that members who receive clear signals from constituents, interest groups, and policy leaders will announce their positions earlier. Those with conflicting signals will seek more information, delaying their announcement. We test several expectations by examining data on when members of the House of Representatives announced their positions on the North American Free Trade Agreement. We also contrast the timing model with a vote model, and find that there are meaningful differences between the factors influencing the timing of position announcements and vote choice. Our research allows analysts to interpret the process leading up to the House action and the end state of that process.
Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory
Authors: Craig William
Published: May 2006

One task of metamathematics is to relate suggestive but nonelementary modeltheoretic concepts to more elementary proof-theoretic concepts, thereby opening up modeltheoretic problems to proof-theoretic methods of attack. Herbrand's Theorem (see [8] or also [9], vol. 2) or Gentzen's Extended Hauptsatz (see [5] or also [10]) was first used along these lines by Beth [1]. Using a modified version he showed that for all first-order systems a certain modeltheoretic notion of definability coincides with a certain proof theoretic notion. In the present paper the Herbrand-Gentzen Theorem will be applied to generalize Beth's results from primitive predicate symbols to arbitrary formulas and terms.

This may be interpreted as showing that (apart from some relatively minor exceptions which will be made apparent below) the expressive power of each first-order system is rounded out, or the system is functionally complete, in the following sense: Any functional relationship which obtains between concepts that are expressible in the system is itself expressible and provable in the system.

A second application is concerned with the hierarchy of second-order formulas. A certain relationship is shown to hold between first-order formulas and those second-order formulas which are of the form (∃T1)…(∃Tk)A or (T1)…(Tk)A with A being a first-order formula. Modeltheoretically this can be regarded as a relationship between the class AC and the class PC⊿ of sets of models, investigated by Tarski in [12] and [13].
The pure calculus of entailment
Authors: Anderson Alan Ross , Belnap Nuel D.
Published: May 2006

The “implicational paradoxes” are treated by most contemporary logicians somewhat as follows:

“The two-valued prepositional calculus sanctions as valid many of the obvious and satisfactory inferences which we recognize intuitively as valid, such as

(A→.B→C)→.A→B→.A→C,2

and

A→B→.B→C→.A→C;

it consequently suggests itself as a candidate for a formal analysis of implication.
Extendible sentential calculus
Authors: Hiz H.
Published: May 2006

The system of sentential calculus presented below has peculiarities which may be of some interest. It is complete in the sense that every classical (two-valued) tautology is provable. In spite of this it is not Post complete (nor is it absolutely complete), i.e., one can add to the system an unprovable formula without proving a sentential variable as a theorem (or without making every formula a theorem). Thus the system may be extended by adjoining an unprovable formula without making the system inconsistent in the Post (or in absolute) sense. There are many distinct extensions of this kind. For every formula α1 that is not a theorem and which adjoined to the system does not make the system Post (or absolutely) inconsistent there is a formula α2 such that adjunction of α2 to the original system leaves α1 unprovable.
Axioms for the “Gergonne”-relations
Authors: thomas Ivo , Orth Don
Published: May 2006

Independence of axioms was not investigated in [Faris]. We show that this quality is lacking, since 2 can be derived from the rest, which without it constitute an independent set. In the proofs of independence it is clearly more informative to decompose 9, C1abKN2abKN3abN5ab and 10, C3abKN2abN5ab into three and two propositions respectively.
On logically false evidence statements
Authors: Leblanc Hugues
Published: May 2006

Logical falsehoods are usually barred in confirmation theory from serving as evidence statements. I wish to study here some three major ways in which this restriction can be lifted.

1. Consider the following axioms for the two-argument confirmation function C:

A1. 0 ≤ C(h, e) ≤ 1;

A2. If ⊦h ≡ h′ and ⊦e ≡ e′, then C(h, e) = C(h′, e′);

A3. If ⊦e ⊃ h, then C(h, e) = 1;

A4. If ⊦e ⊃ ˜(h.h′), then C(h⋁h′, e) = C(h, e)+C(h′, e);

A5. C(h.h′, e) = C(h,e)×C(h′, h.e);

where h, h′, e, and e′ are any four statements from a consistent language L and where ‘⊦’ is short for ‘is logically true in L.’ A1—A5 are consistent, as shown by the following construction:

C1. Let all four of h, h′, e, and e′ be some logical truth lt of L, and let C(h, e) equal 1 for any two h and e;

under which they become true. But they yield as consequences:

and hence

No statement e of L is logically false.

Since all the languages for which confirmation theories have been proposed contain logical falsehoods, (1) is undesirable. Restrictions must accordingly be placed upon some of A1—A5.
A remark on free choice sequences and the topological completeness proofs
Authors: Kreisel G.
Published: May 2006

Below are collected some simple results on the theory of free choice sequences [4] or infinitely proceeding sequences (ips) as they are called in [5]. These results are not sufficient to settle the completeness problems for Heyting's predicate calculus [4], as formulated in [12], neither in the strong nor in the weak sense. They are published because they lead to intuitionistically valid versions of completeness proofs which have appeared in the literature, particularly [16], [17], [18], and, with certain reservations, [1].

The problems considered below (except in §8) differ from those of [12] in the following respect: In [12] we were mainly concerned with formulae of Heyting's predicate calculus which were not even classically provable, and showed that the calculus was complete with respect to certain classes of these formulae. The novel feature was that we established this completeness by means of intuitionistically valid methods, in fact methods which can be formalized in Heyting's arithmetic. Here we are primarily concerned with formulae which are classically, but not intuitionistically, provable. As pointed out in [12], the nature of the completeness problem for such formulae is totally different: the class of predicates which provides the required counterexamples must come from a system (with an intuitionistically acceptable interpretation) which, unlike Heyting's arithmetic, is not a subsystem of the corresponding classical system. An example of such a system is an extension FC, given below, of Heyting's formalization of the theory of free choices.
Degrees of formal systems
Authors: Shoenfield J. R.
Published: May 2006

In this paper we answer some of the questions left open in [2]. We use the terminology of [2]. In particular, a theory will be a formal system formulated within the first-order calculus with identity. A theory is identified with the set of Gödel numbers of the theorems of the theory. Thus Craig's theorem [1] asserts that a theory is axiomatizable if and only if it is recursively enumerable.

In [2], Feferman showed that if A is any recursively enumerable set, then there is an axiomatizable theory T having the same degree of unsolvability as A. (This result was proved independently by D. B. Mumford.) We show in Theorem 2 that if A is not recursive, then T may be chosen essentially undecidable. This depends on Theorem 1, which is a result on recursively enumerable sets of some independent interest.

Our second result, given in Theorem 3, gives sufficient conditions for a theory to be creative. These conditions are more general than those given by Feferman. In particular, they show that the system of Kreisel described in [2] is creative.
A generalization of the concept ofω-completeness
Authors: Henkin Leon
Published: May 2006

The concepts ofω-consistencyandω-completenessare closely related. The former concept has been generalized to notions of Γ-consistencyandstrongΓ-consistency, which are applicable not only to formal systems of number theory, but toallfunctional calculi containing individual constants; and in this general setting the semantical significance of these concepts has been studied. In the present work we carry out an analogous generalization for the concept ofω-completeness.

Suppose, then, thatFis an applied functional calculus, and that Γ is a non-empty set of individual constants ofF. We say thatFis Γ-completeif, wheneverB(x)is a formula (containing the single free individual variablex) such that ⊦B(α) for every α in Γ, then also ⊦(x)B(x). In the paper “Γ-con” a sequence of increasingly strong concepts, Γ-consistency,n= 1,2, 3,…, was introduced; and it is possible in a formal way to define corresponding concepts of Γn-completeness, as follows. We say thatFis Γn-completeif, wheneverB(x1,…,xn) is a formula (containing exactlyndistinct free variables, namelyx1…,xn) such that ⊦B(α1,…,αn) for allα1,…,αnin Γ, then also ⊦ (X1)…(xn)B(x1,…,xn). However, unlike the situation encountered in the paper “Γ-con”, these definitions are not of interest – for the simple reason thatFis Γn-complete if and only if it is Γ-complete, as one easily sees.
Eulerian syllogistic
Authors: Thomas Ivo
Published: May 2006

Faris [1] presents a system for non-void classes employing four primitive functors with another defined, and based on ten asserted and eleven rejected axioms, with a special rule of rejection analogous to Słupecki's for the syllogistic. Primitive functors are here reduced to three, axioms are simplified, and it is shown that the system is decidable by the easier syllogistic means, e.g. the tabular method of Thomas [3].

From the theses (original numbering to the right with axioms starred)

we can deduce
Three theorems on recursive enumeration. I. Decomposition. II. Maximal set. III. Enumeration without duplication
Authors: Friedberg Richard M.
Published: May 2006

In this paper we shall prove three theorems about recursively enumerable sets. The first two answer questions posed by Myhill [1].

The three proofs are independent and can be presented in any order. Certain notations will be common to all three. We shall denote by “Re” the set enumerated by the procedure of which e is the Gödel number. In describing the construction for each proof, we shall suppose that a clerk is carrying out the simultaneous enumeration of R0, R1, R2, …, in such a way that at each step only a finite number of sets have begun to be enumerated and only a finite number of the members of any set have been listed. (One plan the clerk can follow is to turn his attention at Step a to the enumeration of Re where e+1 is the number of prime factors of a. Then each Re receives his attention infinitely often.) We shall denote by “Rea” the set of numbers which, at or before Step a, the clerk has listed as members of Re. Obviously, all the Rea are finite sets, recursive uniformly in e and a. For any a we can determine effectively the highest e for which Rea is not empty, and for any a, e we can effectively find the highest member of Rea, just by scanning what the clerk has done by Step a. Additional notations will be introduced in the proofs to which they pertain.
Elementary completeness properties of intuitionistic logic with a note on negations of prenex formulae
Authors: Kreisel G.
Published: May 2006

The purpose of the present article is to formulate in an intuitionistically meaningful manner the completeness problems for the intuitionistic predicate calculus, and to establish the completeness of certain fragments of it. In these proofs certain translations of classical logic into intuitionistic logic are used, in particular those discovered by Kolmogorov [11] and Gödel [3], and a new one in which negations of prenex formulae are central. Since the last one is of interest also independently of the completeness problems, the details are presented separately at the end of this paper.

All arguments are intended to be intuitionistically valid unless the opposite is stated; in particular, ‘proof’ means intuitionistic proof, and ‘formal proof’ means proof in the relevant system of Heyting [4], [5].

Open problems are mentioned in Remarks 3.1 and 8.1.

German capitals denote formulae of predicate logic, Latin (italic) capitals denote predicate symbols or propositional letters.
Gödel numberings of partial recursive functions
Authors: Rogers Hartley
Published: May 2006

In § 1 we present conceptual material concerning the notion of a Gödel numbering of the partial recursive functions. § 2 presents a theorem about these concepts. § 3 gives several applications. The material in § 1 and § 2 grew out of attempts by the author to find routine solutions to some of the problems discussed in § 3. The author wishes to acknowledge his debt in § 2 to the fruitful methods of Myhill in [M] and to thank the referee for an abbreviated and improved version of the proof for Lemma 3 in § 2.

In the literature of mathematical logic, “Gödel numbering” usually means an effective correspondence between integers and the well-formed formulas of some logical calculus. In recursive function theory, certain such associations between the non-negative integers and instructions for computing partial recursive functions have been fundamental. In the present paper we shall be concerned only with numberings of the latter, more special, sort. By numbers and integers we shall mean non-negative integers. Our notation is, in general, that of [K]. If ϕ and ψ are two partial functions, ϕ = ψ shall mean that (∀x)[ϕ(x)≃(ψx)], i.e., that ϕ and ψ are defined for the same arguments and are equal on those arguments. We consider partial recursive functions of one variable; applications of the paper to the case of several variables, or to the case of all partial recursive functions in any number of variables, can be made in the usual way using the coordinate functions (a)i of [K, p. 230]. It will furthermore be observed that we consider only concepts that are invariant with respect to general recursive functions; more limited notions of Gödel numbering, taking into account, say, primitive recursive structure, are beyond the scope of the present paper.
Splinters of recursive functions
Authors: Ullian J. S.
Published: May 2006

Basic notation in this paper is as in [3]. From [5] and [9] the following additional notation is derived,ϕiis the partial recursive function with indexi, Wiits range. ∅ is the empty set. ‘≡’ denotes isomorphism between sets, ‘≡m’ many-one equivalence, ‘≡T’ Turing equivalence, ‘≦1’ and ‘≦m’ signify one-one and many-one reducibility respectively. ‘Recursive’ is used throughout for ‘general recursive’.
The separation theorem of intuitionist propositional calculus
Authors: Horn Alfred
Published: May 2006

A standard set of axioms for the intuitionist propositional calculus is the following (we associate to the right, and use the convention that ⊃ binds less strongly than the other connectives).
A completeness theorem in modal logic
Authors: Kripke Saul A.
Published: May 2006

The present paper attempts to state and prove a completeness theorem for the system S5 of [1], supplemented by first-order quantifiers and the sign of equality. We assume that we possess a denumerably infinite list of individual variables a, b, c, …, x, y, z, …, xm, ym, zm, … as well as a denumerably infinite list of n-adic predicate variables Pn, Qn, Rn, …, Pmn, Qmn, Rmn,…; if n=0, an n-adic predicate variable is often called a “propositional variable.” A formula Pn(x1, …,xn) is an n-adic prime formula; often the superscript will be omitted if such an omission does not sacrifice clarity.
Constructive definition of certain analytic sets of numbers
Authors: Lorenzen P. , Myhill J.
Published: May 2006

According to Kleene [8] and Post [13] the definition of recursive relations (or sets) can be given most simply via the definition of recursively enumerable (r.e.) relations. The latter can be defined by finite systems of finite rules for deriving strings of symbols, each rule being of the form

each formula or being obtained by juxtaposition from atomic symbols and variables ranging over strings of atomic symbols.
“Aiming at a Moving Target”: Social Science and the Recent Rebellions in Eastern Europe
Authors: Tarrow Sidney
Published: May 2006

One week before the mass demonstrations that led to the collapse of the Czechoslovak Communist regime in November, 1989, a Charter 77 activist, Jan Urban, proposed that the group contest the national elections to be held in June of 1991. Urban's friends laughed at his proposals for being hopelessly Utopian. But a week later, thousands of students filled Wenceslas Square, a general strike was called, and the regime collapsed. The leaders of the future Civic Forum, who had been carefully watching events in Hungary, Poland and the GDR, had little idea that their own country was ripe for revolution.

Charter 77 would not have fared much better had it consulted Western social scientists, because our models for understanding the emergence of new social movements and their spread and outcomes are woefully inadequate. While prediction in social science is always hazardous, our lack of preparation for the recent wave of mobilization in Eastern Europe is particularly glaring, given the vast body of research and theorizing that has developed since the 1960s both in Western Europe and the United States.
Doing “Tuesday Lunch” at Lyndon Johnson's White House: New Archival Evidence on Vietnam Decisionmaking
Authors: Barrett David M.
Published: May 2006

Over the past decade, a number of political scientists have employed presidential papers and other archival materials in order to test various hypotheses regarding American politics. This has been particularly true concerning the Vietnam War and the American presidency (Kahin 1986; Burke and Greenstein 1989; Berman 1982, 1989; Kolko 1985; Hatcher 1990), as scholars have explored the interconnections between ideology, political style, presidential character, and other variables which may explain America's participation in that war. Thus, while some in the profession may have disdained the use of traditional historical research and methodology, there clearly has been a modest resurgence of archival research for the purposes of theory building.

While I am among those who see real possibilities for illuminating political processes by drawing on archival sources, their usefulness should not be overstated: even rich archival collections-may not “solve” debates over causation of political phenomena.
The Effects of the Thomas Appointment to the Supreme Court
Authors: O'Connor Karen
Published: May 2006

In announcing his nomination of Clarence Thomas to the United States Supreme Court on July 2, 1991, George Bush described him as “a fiercely independent thinker with an excellent legal mind,” and proclaimed his belief that Thomas would “be a great Justice.” While many legal and political commentators had predicted that Clarence Thomas stood an excellent chance of being Bush's nominee to replace the retiring Thurgood Marshall, few were quick to echo Bush's assessment that Thomas was:

… the best qualified at this time …. Clarence Thomas … fits my description of the best man at the right time. … I kept my word to the American people and to the Senate by picking the best man for the job on the merits. (New York Times, 2 July 1991)

Even as Bush offered Thomas's name in nomination, the skeptics were muttering about the hyperbole that surrounded the announcement. Thomas's total lack of courtroom experience and his generally undistinguished record as a jurist led many to question his qualifications to serve on the High Court. Concern with his general absence of legal credentials prompted the American Bar Association's Standing Committee on the Federal Judiciary to rate Thomas merely as “Qualified”—making him the only nominee with such a low rating to serve on the Supreme Court.

The authority and prestige of the United States Supreme Court have always rested on its support from the other branches of government and, perhaps even more importantly, on the support of the American public.
Gender Roles and UN Reform
Authors: Galey Margaret E.
Published: May 2006

Reform has been an important theme within the United Nations during the decade of the 1980s. That decade has witnessed both the continuation of efforts towards structural reform initiated over thirty years ago as well as the beginning of a rather different species of reform, movement towards reshaping the relationships between men and women within societies whose governments make up official members of the world organization. The latter is reflected most recently in the Forward Looking Strategies for the Advancement for Women to the Year 2000 (FLS), the set of guidelines approved by consensus by 159 government delegates at the 1985 UN World Conference on the UN Decade for Women in Nairobi, Kenya in 1985. Though not designated a “reform program,” the FLS contains a set of recommendations which if implemented could contribute to the reform or reshaping of the sex-gender system that characterizes the relations of men and women in public and private institutions within societies throughout the world. In this respect, it is interesting that three prominent American women politicians played key roles in traditional UN reform and with respect to the adoption of the FLS at Nairobi: Maureen Reagan, who headed the U.S. delegation to Nairobi and subsequently served as U.S. Representative to the UN Commission on the Status of Women; Jeanne Kirkpatrick, the first American woman to hold the position of U.S./UN Ambassador; and Sen. Nancy Kassebaum, Republican Senator from Kansas, the only woman member of the Senate Foreign Relations Committee.