bluuebunny/crossref_metadata_2025 huggingface dataset:
Finite sets and frege structures
Authors: Bell John L.
Published: May 2006

Call a family of subsets of a set E inductive if and is closed under unions with disjoint singletons, that is, if

A Frege structure is a pair (E, ν) with ν a map to E whose domain dom(ν) is an inductive family of subsets of E such that

In [2] it is shown in a constructive setting that each Frege structure determines a subset which is the domain of a model of Peano's axioms. In this note we establish, within the same constructive setting, three facts. First, we show that the least inductive family of subsets of a set E is precisely the family of decidable Kuratowski finite subsets of E. Secondly, we establish that the procedure presented in [2] can be reversed, that is, any set containing the domain of a model of Peano's axioms determines a map which turns the set into a minimal Frege structure: here by a minimal Frege structure is meant one in which dom(ν) is the least inductive family of subsets of E. And finally, we show that the procedures leading from minimal Frege structures to models of Peano's axioms and vice-versa are mutually inverse. It follows that the postulation of a (minimal) Frege structure is constructively equivalent to the postulation of a model of Peano's axioms.

All arguments will be formulated within constructive (intuitionistic) set theory.
Adjoining cofinitary permutations
Authors: Zhang Yi
Published: May 2006

We show that it is consistent with ZFC + ¬CH that there is a maximal cofinitary group (or, maximal almost disjoint group) G ≤ Sym(ω) such that G is a proper subset of an almost disjoint family A ⊆ Sym(ω) and ‖G‖ < ‖A‖. We also ask several questions in this area.
The representation theories of elementarily equivalent rings
Authors: Prest Mike
Published: May 2006

Two rings are elementarily equivalent if and only if they satisfy the same sentences in the language of rings. To some extent this is reflected in the representation theories of the two rings (one may see both positive and negative results along these lines in [5]). Here we concentrate on the case of a ring S and an elementary subring R of S.

We show that if R is an elementary subring of S then the lattice of pp formulas for R-modules embeds in that for S-modules. These lattices, moreover, have the same finite sub-posets. From this we derive some corollaries. Then we consider to what extent the compositions of induction and restriction between R- and S-modules preserve elementary equivalence.
On the computational content of the axiom of choice
Authors: Berardi Stefano , Bezem Marc , Coquand Thierry
Published: May 2006

We present a possible computational content of the negative translation of classical analysis with the Axiom of (countable) Choice. Interestingly, this interpretation uses a refinement of the realizability semantics of the absurdity proposition, which is not interpreted as the empty type here. We also show how to compute witnesses from proofs in classical analysis of ∃-statements and how to extract algorithms from proofs of ∀∃-statements. Our interpretation seems computationally more direct than the one based on Gödel's Dialectica interpretation.
Chang's Conjecture and the Non-Stationary Ideal
Authors: Seabold Daniel Evan
Published: May 2006

In The Axiom of Determinacy, Forcing Axioms and the Nonstationary Ideal [W1], Woodin constructs the partial order ℙmax, which in the presence of large cardinals yields a forcing extension of L(ℝ) where ZFC holds and the non-stationary ideal on ω1 (hereafter denoted NSω1) is ω2-saturated. The basic analysis of ℙmax forcing over L(ℝ) can be carried out assuming only the Axiom of Determinacy (AD). In the central result of this paper, we show that if one increases slightly the strength of the determinacy assumptions, then Chang's Conjecture—the assertion that every finitary algebra on ω2 has a subalgebra of order type ω1—holds in this extension as well. Specifically, we obtain:

Corollary 4.6. Assume AD + V = L(ℝ, μ) + μ is a normal, fine measure on. Chang's Conjecture holds in any ℙmax-generic extension of L(ℝ).

This technique for obtaining Chang's Conjecture is fairly general. We [Se] have adapted it to obtain Chang's Conjecture in the model presented by Steel and Van Wesep [SVW] and Woodin [Wl] has adapted it to his ℚmax forcing notion. In each of these models, as in the ℙmax extension, one forces over L(ℝ) assuming AD to obtain ZFC and NSω1 is ω2-saturated.

By unpublished results of Woodin, the assumption for Corollary 4.6 is equiconsistent with the existence of ω2 many Woodin cardinals, and hence strictly stronger than ADL(ℝ). One would like to reduce this assumption to ADL(ℝ). Curiously, this reduction is not possible in the arguments for ℚmax or the Steel and Van Wesep model, and the following argument of Woodin suggests why it may not be possible for ℙmax either.
On the admissible rules of intuitionistic propositional logic
Authors: Iemhoff Rosalie
Published: May 2006

We present a basis for the admissible rules of intuitionistic propositional logic. Thereby a conjecture by de Jongh and Visser is proved. We also present a proof system for the admissible rules, and give semantic criteria for admissibility.
Distance semantics for belief revision
Authors: Lehmann Daniel , Magidor Menachem , Schlechta Karl
Published: May 2006

A vast and interesting family of natural semantics lor belief revision is defined. Suppose one is given a distance d between any two models. One may then define the revision of a theory K by a formula α as the theory defined by the set of all those models of α that are closest, by d. to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates describe properties of iterated revisions.
Degree spectra of intrinsically c.e. relations
Authors: Hirschfeldt Denis R.
Published: May 2006

We show that for every c.e. degreea>0there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is {0, a}. This result can be extended in two directions. First we show that for every uniformly c.e. collection of setsSthere exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is the set of degrees of elements ofS. Then we show that ifα∈ω∪ {ω} then for anyα-c.e. degreea>0there exists an intrinsicallyα-c.e. relation on the domain of a computable structure whose degree spectrum {0, a}. All of these results also hold for m-degree spectra of relations.
Some interesting connections between the slow growing hierarchy and the Ackermann function
Authors: Weiermann Andreas
Published: May 2006

It is shown that the so called slow growing hierarchy depends non trivially on the choice of its underlying structure of ordinals. To this end we investigate the growth rate behaviour of the slow growing hierarchy along natural subsets of notations for Γ0. Let T be the set-theoretic ordinal notation system for Γ0 and Ttree the tree ordinal representation for Γ0. It is shown in this paper that (Gα)α∈T matches up with the class of functions which are elementary recursive in the Ackermann function as does (by folklore). By thinning out terms in which the addition function symbol occurs we single out subsystems T* ⊆ T and Ttree* ⊆ Ttree (both of order type not exceeding ε0) and prove that still matches up with but now consists of elementary recursive functions only. We discuss the relationship between these results and the Γ0-based termination proof for the standard rewrite system for the Ackermann function.
Supercompactness within the projective hierarchy
Authors: Becker Howard , Jackson Steve
Published: May 2006

We show that all the projective ordinals are supercompact through their supremum and a ways beyond.
Small profinite groups
Authors: Newelski Ludomir
Published: May 2006

We propose a model-theoretic framework for investigating profinite groups. Within this framework we define and investigate small profinite groups. We consider the question if any small profinite group has an open abelian subgroup.
An almost deep degree
Authors: Cholak Peter , Groszek Marcia , Slaman Theodore
Published: May 2006

We show there is a non-recursive r.e. set A such that if W is any low r.e. set. then the join W ⊕ A is also low. That is. A is “almost deep”. This answers a question of Joekusch. The almost deep degrees form an definable ideal in the r.e. degrees (with jump.)
Admissibility of structural rules for contraction-free systems of intuitionistic logic
Authors: Dyckhoff Roy , Negri Sara
Published: May 2006

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculusG4ipfor intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs, i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.
Expedited Broda-Damas bracket abstraction
Authors: Bunder M. W.
Published: May 2006

A bracket abstraction algorithm is a means of translating λ-terms into combinators. Broda and Damas, in [1], introduce a new, rather natural set of combinators and a new form of bracket abstraction which introduces at most one combinator for each λ-abstraction. This leads to particularly compact combinatory terms. A disadvantage of their abstraction process is that it includes the whole Schönfinkel [4] algorithm plus two mappings which convert the Schönfinkel abstract into the new abstract. This paper shows how the new abstraction can be done more directly, in fact, using only 2n − 1 algorithm steps if there are n occurrences of the variable to be abstracted in the term. Some properties of the Broda-Damas combinators are also considered.
Unfoldable cardinals and the GCH
Authors: Hamkins Joel David
Published: May 2006

Unfoldable cardinals are preserved by fast function forcing and the Laver-like preparations that fast functions support. These iterations show, by set-forcing over any model of ZFC, that any given unfoldable cardinal κ can be made indestructible by the forcing to add any number of Cohen subsets to κ.
Decidable fragments of first-order modal logics
Authors: Wolter Frank , Zakharyaschev Michael
Published: May 2006

The paper considers the setof first-order polymodal formulas the modal operators in which can be applied to subformulas of at most one free variable. Using a mosaic technique, we prove a general satisfiability criterion for formulas in, which reduces the modal satisfiability to the classical one. The criterion is then used to single out a number of new, in a sense optimal, decidable fragments of various modal predicate logics.
The Relative-Gains Problem for International Cooperation
Authors: Grieco Joseph , Powell Robert , Snidal Duncan
Published: May 2006

Modern realism claims that the fear that others will enjoy relatively greater benefits frequently impedes international cooperation. Recent articles in thisReviewby Duncan Snidal and Robert Powell modeled conditions under which the impact of relative gains varied. Joseph Grieco criticizes Snidal's model as based on assumptions that allow him to avoid, rather than confront, the realist arguments. He also argues that Powell's model, while constructive, ignores important additional sources of sensitivity to relative gains. In response, Powell discusses the value of alternative assumptions about preferences and constraints in international relations. Snidal defends his analysis and presents an additional proof to support the independence of his central result—the diminishing impact of relative gains with increasing numbers of states—from assumptions of concern to Grieco. Both responders emphasize their work as contributing to a contextually rich theory of international politics that builds on elements of both realism and neo-liberalism.
Party Platforms, Mandates, and Government Spending
Authors: King Gary , Laver Michael , Hofferbert Richard I. , Budge Ian , McDonald Michael D.
Published: May 2006

In their 1990 Review article, Ian Budge and Richard Hofferbert analyzed the relationship between party platform emphases, control of the White House, and national government spending priorities, reporting strong evidence of a “party mandate” connection between them. Gary King and Michael Laver successfully replicate the original analysis, critique the interpretation of the causal effects, and present a reanalysis showing that platforms have small or nonexistent effects on spending. In response, Budge, Hofferbert, and Michael McDonald agree that their language was somewhat inconsistent on both interactions and causality but defend their conceptualization of “mandates” as involving only an association, not necessarily a causal connection, between party commitments and government policy. Hence, while the causes of government policy are of interest, noncausal associations are sufficient as evidence of party mandates in American politics.
The Impact of the Gulf War on the Ingredients of Presidential Evaluations: Multidimensional Effects of Political Involvement
Authors: Krosnick Jon A. , Brannon Laura A.
Published: May 2006

When the United States began its overt military conflict with Iraq in January 1991, the news media focused unceasingly on the Gulf crisis. Using national survey data, we show that this emphasis altered the ingredients of Americans' assessments of George Bush's performance. After the war, assessments were based more on beliefs about Bush's effectiveness in managing the conflict and less on confidence in his handling of other foreign relations matters or the domestic economy. Consequently, Bush's overall performance ratings increased dramatically following the war. We also show that the media's impact on political judgments was regulated by citizens' levels of political knowledge, exposure to political news, and interest in the war. Greater impact was associated with higher levels of knowledge and lower levels of exposure and interest. These findings challenge traditional views of these dimensions of political involvement and support a view derived from contemporary psychological theories of information processing.
Is Talk Really Cheap? Prompting Conversation between Critical Theory and Rational Choice
Authors: Johnson James
Published: May 2006

Critical theory and rational choice theory share both overlapping concerns and parallel theoretical weaknesses. Specifically, both critical theorists and rational choice theorists are preoccupied with determining whatrationalcan mean in the realm of social and political interaction. I show in a provisional way how game theory extends and deepens the critical theorists' basic intuition that unembellished strategic rationality cannot adequately sustain social and political interaction. And I suggest how critical theory identifies a mechanism underlying the force of the “cheap talk” that game theorists introduce in hopes of circumscribing the indeterminacy generated by their models. My goal is to stimulate productive conversation between what are typically considered discordant research traditions.
The Political Economy of Elections in Latin America, 1980–1991
Authors: Remmer Karen L.
Published: May 2006

The process of political democratization in Latin America during the 1980s created a rare opportunity to explore the political economy of elections outside of the North Atlantic basin. Using interrupted time-series analysis, I explore the impact of elections on macroeconomic performance in eight Latin American nations. The findings indicate that macroeconomic performance has fluctuated with the electoral calendar but that contrary to the traditional business cycle literature, as well as the conventional wisdom about Latin America, competitive elections have enhanced, rather than undermined, the capacity of political leaders to address outstanding problems of macroeconomic management. The analysis suggests that the relationship between democracy and economics is captured more adequately by a “political capital” model than by its traditional theoretical alternative.
Sectionalism in Congress (1870 to 1890)
Authors: Roach Hannah Grace
Published: May 2006

Sectionalism is a fundamental and persistent factor in American politics. In the shaping of congressional legislation and even in the formation of the platforms of our national parties, the influence of conflicting sectional interests is of prime importance. The precise nature of such sectional conflicts and the alignment of the various sections upon the leading policies of the time are clearly revealed by an analysis of the votes and debates in Congress on outstanding issues of national importance. Such votes, mapped by congressional districts, show that again and again party lines are broken by the force of sectional interest and that both Republicans and Democrats divide into sectional wings.

A study of the period from the early 1870's to 1890 shows that sectionalism at that time was in large measure the product of the interaction of two movements in our national development,—the rapid expansion of Western settlement, particularly in the trans-Mississippi Middle West (the West North Central states) and the Mountain region, and the marked intensification of industrialism in the older sections of the country, especially in the North Atlantic states. Sectional alliances are flexible and shift with changing economic conditions. The East North Central states, for example, which at the beginning of the period usually vote in alliance with the West North Central and South, by the later eighties are found often on the side of the North Atlantic, a change which may be due to the fact that in the interval they had undergone a marked industrial development which gave them economic interests in common with the older sections. The areas of strongest radical voting move farther West with the shift in the centres of production of grain and livestock; that is, the nucleus of revolt in the Western wing of the Republican party especially is in the newer agricultural regions.
Economic Security and Value Change
Authors: Inglehart Ronald , Abramson Paul R.
Published: May 2006

Confirming Inglehart's prediction (1971) of an intergenerational shift toward postmaterialist values, a time series analysis controlling for the joint effects of inflation and unemployment demonstrates that there is a statistically significant trend toward postmaterialism in all eight West European countries for which data are available over the past two decades. Evidence from the 1981–83 and 1990–91 World Values Surveys indicates that this value shift occurs in any society that has experienced sufficient economic growth in recent decades so that the preadult experiences of younger birth cohorts were significantly more secure than those of older cohorts. Large intergenerational differences tend to be found in societies that have experienced rapid growth in gross national product per capita, and are negligible in societies that have had little or no growth. Accordingly, postmaterialism increased in 18 of the 20 societies on five continents for which we have comparable data over the past decade.
Strategic Voting Equilibria under the Single Nontransferable Vote
Authors: Cox Gary W.
Published: May 2006

Previous investigations of strategic voting equilibria in mass electorates have looked only at single-member districts. I shall investigate such equilibria in multimember districts operating under the single nontransferable vote system. What appear to be the most natural equilibria conform to the M + 1 rule, according to which strategic voting in M-seat districts produces exactly M + 1 vote-getting candidates in equilibrium, any others having their support totally undercut. This result provides the beginnings of a formal underpinning for Reed's recent extension of Duverger's Law to the Japanese case. The model also generates specific and empirically testable hypotheses concerning the exceptions to the M + 1 rule that one ought to expect in equilibrium. I test these hypotheses with Japanese data. Finally, the model also reveals a type of strategic voting that is specific to multimember districts. I use Japanese data again to explore the empirical importance of this kind of strategic voting.
The Piety of Thought in Plato'sRepublic, Book 1
Authors: Dobbs Darrell
Published: May 2006

In the opening sentence of theRepublic, Socrates recounts his intention to combine the operations of piety and theoretical speculation. Nevertheless, many readers regard Cephalus' subsequent abandonment of rational inquiry to perform certain sacred rites as a definitive indication of Plato's opinion that piety and philosophy are fundamentally incompatible. I find this interpretation untenable inasmuch as it depends upon the misidentification of Cephalus as the dialogue's representative of piety. I suggest that the true nature and philosophical significance of piety are indicated instead in Socrates' conversation with Cephalus' son, Polemarchus. As this conversation unfolds, Polemarchus' pious inclinations culminate in a perception of the dearness of the unknown good. Inspired by this piety, Socrates and Polemarchus defend the conventional paragon Simonides and, at the same time, launch a truly philosophical inquiry into justice.
Electoral Competition with Informed and Uninformed Voters
Authors: Baron David P.
Published: May 2006

I present a model of electoral competition in which candidates raise campaign contributions by choosing policies that benefit interest groups and then expend those contributions to influence voters who are uninformed about the policies. Informed voters, however, vote based on those policies, so candidates face a trade-off between choosing a policy to generate funds to attract the uninformed vote and choosing a policy to attract the informed vote. Electoral equilibria are characterized for two categories of policies: particularistic and collective. In the case of particularistic policies, the equilibrium policies of the candidates are separated if the proportion of uninformed voters is sufficiently high, and the degree of separation is an increasing function of that proportion. The model is extended to include the public financing of elections and incumbency advantages. For the case of collective policies, the candidates locate at the median of the ideal points of the informed voters, and contributions are zero.
Explaining Interethnic Cooperation
Authors: Fearon James D. , Laitin David D.
Published: May 2006

Though both journalists and the academic literature on ethnic conflict give the opposite impression, peaceful and even cooperative relations between ethnic groups are far more common than is large-scale violence. We seek to explain this norm of interethnic peace and how it occasionally breaks down, arguing that formal and informal institutions usually work to contain or “cauterize” disputes between individual members of different groups. Using a social matching game model, we show that local-level interethnic cooperation can be supported in essentially two ways. Inspiral equilibria, disputes between individuals are correctly expected to spiral rapidly beyond the two parties, and fear of this induces cooperation “on the equilibrium path.” Inin-group policing equilibria, individuals ignore transgressions by members of the other group, correctly expecting that the culprits will be identified and sanctioned by their own ethnic brethren. A range of examples suggests that both equilibria occur empirically and have properties expected from the theoretical analysis.
Partisan Effects of Voter Turnout in Senatorial and Gubernatorial Elections
Authors: Nagel Jack H. , McNulty John E.
Published: May 2006

Conventional wisdom holds that higher turnout favors Democrats. Previous studies of this hypothesis rely on presidential and House elections or on survey data, but senatorial and gubernatorial elections offer better conditions for directly testing turnout effects in U.S. politics. In a comprehensive analysis of these statewide elections since 1928, we find that the conventional theory was true outside the South through 1964, but since 1965 the overall relationship between turnout and partisan outcomes has been insignificant. Even before the mid-1960s, the turnout effect outside the South was strongest in Republican states and insignificant or negative in heavily Democratic states. A similar but weaker pattern obtains after 1964. In the South, which we analyze only since 1966, higher turnout helped Republicans until 1990, but in 1990–94 the effect became pro-Democratic. The conventional theory cannot account for these complex patterns, but they are impressively consistent with DeNardo's (1980) theory.
Myth and Reality in Business Support for Democrats and Republicans in the 1936 Presidential Election
Authors: Webber Michael J. , Domhoff G. William
Published: May 2006

Using campaign contributions by business leaders as an indicator of their political preferences, this paper tests two different claims concerning the 1936 presidential elections: (1) Business leaders in mass-consumption industries differentially favored the Democrats for reasons of economic policy; and (2) business leaders in capital-intensive and internationally oriented industries differentially favored the Democrats for reasons of economic policy. The paper shows that in the 1936 election no industrial sector was more likely to support the Democrats when region, religion, and the special circumstances of the brewing industry (gratitude toward the Democrats for ending Prohibition) are taken into consideration. Democratic financial support came predominantly from southerners, members of the Jewish community, officers and directors of smaller businesses, and top-level business leaders from New York City.
The Correlates of Change in International Financial Regulation
Authors: Quinn Dennis
Published: May 2006

With which political and economic variables is change in international financial regulation robustly associated? I undertook multivariate regression analysis of this question using a quantitative measure of the regulation of international financial transactions. The measure was created by coding the laws of 64 nations. The associations between change in international financial regulation and measures of long-run economic growth, corporate taxation, government expenditures, and income inequality are estimated, using the models, methods, and data of Batro (1991), Deininger and Squire (1996a), Leamer (1983, 1985), and Levine and Renelt (1992). The findings point to a new agenda for research on international financial regulation.
Hegel and the Ontological Critique of Liberalism
Authors: Kaufman Alexander
Published: May 2006

Contemporary communitarians argue that a proper consideration of ontological questions of identity and community forecloses deontological liberalism as a viable option, since deontological liberalism cannot ground a sufficiently strong form of immediate identification with the ethical life of the community. Hegel's ethical theory constitutes perhaps the most fully realized account of such identification. Yet, I argue, Hegel's ethics does not require the strong form of immediate identification required by communitarians. My analysis emphasizes the strands in Hegel's account which suggest that a weaker form of identification, reconcilable with deontological liberalism, can plausibly ground a stable form of civil society. In particular, Hegel's notion of patriotic trust is designed to ground both a direct and a reflective relation between individuals and their ethical and political tradition. Hegel's analysis anticipates and offers insights to supplement recent accounts of trust as a form of social capital.
Culture and the Environment in the Pacific Northwest
Authors: Ellis Richard J. , Thompson Fred
Published: May 2006

Douglas and Wildavsky argue that environmental activism is rooted in an egalitarian cultural bias. Others, like Paehlke, counter that environmental commitments and concerns are autonomous from redistributive concerns. Students of the “New Politics” agree that environmentalism is autonomous from conventional left-right distributive concerns but also argue that environmental attitudes and beliefs are embedded in “postmaterial” values, such as citizen participation. Still other scholars emphasize a cultural consensus around environmental values and beliefs. What distinguishes environmental activists, in this view, is less what they believe than their willingness to make sacrifices for those values and beliefs. Drawing upon several surveys of environmental groups and the mass public in the Pacific Northwest, we test these four hypotheses and find that the Douglas-Wildavsky “cultural theory,” although not without its limitations, appears to provide the more satisfactory account of environmental preferences.
Crime and Punishment: The Role of Norms in Crisis Bargaining
Authors: Gelpi Christopher
Published: May 2006

In this work I test the proposition that normative standards of behavior can influence state actions in security-related conflicts. Specifically, I examine the construction of norms in the settlements of security-related disputes and the effects these settlements have on subsequent militarized interactions. I argue that dispute settlements alter subsequent crisis bargaining in two important ways. First, they act as normative referents that alter the interpretation of subsequent crisis bargaining behavior both by identifying a solution to the dispute which alleviates fears of demands for future concessions and by defining a set of acts which both sides consider illegitimate. Second, in combination with the response to their violation, dispute settlements inflict reputational costs on states that violate them. I test these arguments against a realist theory of crisis bargaining through an analysis of 122 reinitiated international crises between 1929 and 1979. I find strong support for the hypothesis that states can and do construct normative standards that guide their behavior in international crises, whereas realist theory receives only mixed support.
The Public Consequences of Private Inequality: Family Life and Citizen Participation
Authors: Burns Nancy , Schlozman Kay Lehman , Verba Sidney
Published: May 2006

This study uses regression analysis of data from a telephone survey of 380 married couples to subject to rare empirical test the contention that, because women are unequal at home, they cannot be equal in the polity. The argument is often made that wives' disadvantage in comparison to their husbands with respect to control over family income, availability of free time, power over decisions, or mutual respect dampens their ability to participate fully in politics. In fact, domestic inequalities do have implications for political activity, but these effects differ from what is usually posited by being stronger for husbands than for wives. For husbands, control over major financial decisions and autonomy in using small amounts of time enhance their ability to participate in politics beyond what would be expected on the basis of their other characteristics. In short, being boss at home is politically empowering to husbands.
Syntactical and semantical properties of simple type theory
Authors: Schütte Kurt
Published: May 2006

In my paper [10] I introduced the syntactical concepts “positive part” and “negative part” of logical formulas in first-order predicate calculus. These concepts make it possible to establish logical systems on inference rules similar to Gentzen's inference rules but without using the concept “sequent” and without needing Gentzen's structural inference rules. Proof-theoretical investigations of several formal systems based on positive and negative parts are published in [11]. In this paper I consider a similar formal system of simple type theory.

A syntactical concept of “strict derivability” results from the formal system in [10] by generalization of the axioms and inference rules from first to higher-order predicate calculus and by addition of inference rules for set abstraction by means of a λ-symbol which allows us to form set expressions of arbitrary types from well-formed formulas.
On formulas of one variable in intuitionistic propositional calculus
Authors: Nishimura Iwao
Published: May 2006

McKinsey and Tarski [3] described Gödel's proof that the number of Brouwerian-algebraic functions is infinite. They gave an example of a sequence of infinitely many distinct Brouwerian-algebraic functions of one argument, which means that there are infinitely many non-equivalent formulas of one variable in the intuitionistic propositional calculus LJ of Gentzen [1]. However they did not completely characterize such formulas. In § 1 of this note, we define a sequence of basic formulas P∞(X), P0(X), P1(X), … and prove the following theorems.
Can the logic of indirect discourse be formalised?
Authors: Cohen L. Jonathan
Published: May 2006

Recent attempts to analyse or explicate assertion-statements and other kinds of indirect discourse in formal terms seem to have overlooked an even greater difficulty than the familiar problems arising about equivalence, synonymy, translatability, etc. This difficulty is created by the fact that in judicial, journalistic, or historical fact-finding, as well as in everyday conversation, we frequently cite statements about a witness's truthfulness alongside the report of his testimony as the premisses from which we argue about the facts. It is then an essential part of our argument that it should appear to jump from one level of statement to another, and perhaps back again. So that the difficulty emerges: how can the formalisation of such an argument adopt any of the usual hierarchy-principles as a guarantee against semantical antinomies?

Consider, for example,

If the policeman testifies that anything, which the prisoner deposes, is false, and the prisoner deposes that something, which the policeman testifies, is true, then something, which the policeman testifies, is false and something, which the prisoner deposes, is true.
Disjunction and existence under implication in elementary intuitionistic formalisms
Authors: Kleene S. C.
Published: May 2006

Let Pp, Pd, and N be the intuitionistic formal systems of prepositional calculus, predicate calculus, and elementary number theory, respectively.1 Consider the following six propositions.8

(1) ├A V B only if ├A or ├B.

(2) ├∋xA(x) only if ├Ã(t) for some formula Ã(x) congruent to A(x) and some term t free for x in Ã(x).
A criterion for completeness of degrees of unsolvability
Authors: Friedberg Richard
Published: May 2006

Kleene and Post [2] have shown that between each degree a and its completion a′ there are an infinity of mutually incomparable degrees of unsolvability, and that between a and its nth. completion a(n) there are an infinity of mutually incomparable degrees each incomparable with a′, …, a(n−1). They have left open the following questions: whether there exist complete degrees in similar profusion; whether indeed there exist incomparable complete degrees at all; and whether certain degrees, such as a(ω) ([2] p. 401), are complete. All these questions are answered affirmatively by the corollary of the present paper, which states that every degree greater than or equal to 0′ is complete. Since every complete degree is already known to be greater than or equal to 0′, it follows from the present paper that being greater than or equal to 0′ is both a necessary and a sufficient condition for completeness.
A formalization of inductive logic
Authors: Martin R. M.
Published: May 2006

In this note we show how Carnap's theory of degree of confirmation (inductive logic) may be constructed upon a very simple and restricted semantical basis. The semantical meta-languages here may either be based upon a relation ofmultiple denotationor may even benon-translational. To these meta-languages a suitable metric for sentences may be appended. Axioms for such meta-languages are suggested, so that an especially simple formalization of Carnap's inductive logic is in effect presented in outline.

For Carnap, inductive logic consists, roughly speaking, of a semantics augmented by a metric. More specifically, for a finite object-languagethe semantics consists of a theory of designation for, and to this are added numerical functions on sentences oftaking real numbers as values. (, it will be recalled, contains justNdistinct individual constants as primitive, where ‘N’ is a constant standing for some fixed finite number.contains a denumerable infinity of distinct individual constants as primitive, and will be discussed in a moment.) Were we to formalize this theory we should have, then, a translation of(or justitself), a syntax for, a primitive relation of designation, real numbers, and several different kinds of class and relational variables. The character of the underlying syntax is not clear from Carnap's account, but this can easily be supplied by a suitable adaptation of Tarski's method. For this, variables for classes of and relations between the expressions of the object-language are needed. Also in Carnap's theory of designation, variables over relations between expressions and objects are needed fundamentally. Real numbers may be handled in various ways. To simplify, let us suppose these are introduced by having a special kind of variable to range over them. Then suitable axioms for real numbers may be given, e.g., one of the axiom sets of Tarski.
An extensional variety of extended basic logic
Authors: Fitch Frederic B.
Published: May 2006

The system K′ of “extended basic logic” lacks a principle of extensionality. In this paper a system KE′ will be presented which is like K′ in many respects but which does possess a fairly strong principle of extensionality by way of rule 6.37 below. It will be shown that KE′ is free from contradiction. KE′ is especially well suited for formalizing the theory of numbers presented in my paper, On natural numbers, integers, and rationals. The methods used there can be applied even more directly here because of the freedom of KE′ from type restrictions, but the details of such a derivation of a portion of mathematics will not be presented in this paper. It is evident, moreover, that KE′ contains at least as much of mathematical analysis as does K′, and perhaps considerably more. The method of carrying out proofs in KE′ is closely similar to that used in my book Symbolic logic, and could be expressed in similar notation.
On intermediate propositional logics
Authors: Umezawa Toshio
Published: May 2006

By intermediate prepositional logics we mean prepositional logics between the intuitionistic and classical logics.

K. Gödel [1] proved that there is a set of intermediate prepositional logics which possesses the order type ω. The method enables us to define intermediate logics in terms of axioms and rules of inference. We shall call it the axiomatic method.
The Economics of Transitions Democracy
Authors: Bates Robert H.
Published: May 2006

This paper explores the relationship between economics and politics in the creation of democracy. The first section examines the shaping influence of the revenue imperative; the second, of end-game bargaining between retreating despots and insurgent democrats; and the third, of human capital. The paper is informal in argument and playful in spirit. It is designed to stimulate and provoke rather than to educate and inform.

I do, however, seek to maintain a consistent set-up for the analysis: On one side stands a sovereign—in an earlier period, most likely a monarch; in the present typically a political party. The sovereign maintains a monopoly over the formulation of public policy and possesses the power to extract resources from the economy. On the other side stand the citizens. They own the factors of production: land, labor, and capital. They care about public policy, but they cannot make it. However, the decisions they do make influence the level of economic resources that can effectively be mobilized by the sovereign.
Presidential Prerogative Power: The Case of the Bush Administration and Legislative Power
Authors: Spitzer Robert J.
Published: May 2006

Both the campaign and early administration of George Bush trumpeted a theme of a more centrist, lower-volume, less confrontational approach to politics and governing. Aspects of both the campaign and the administration seemed to belie this pledge, from the Willie Horton ads to the fight over the Tower nomination and the invasion of Panama. Still, the prevailing tone and style of the Bush administration during its first year seemed far less strident than that of the Reagan era. As Edwards (1989, 3) noted, “Bush has worked diligently to create an atmosphere of reconciliation and goodwill” and has sought to avoid “politically-charged polemics.”

Yet in another respect, the Bush administration seems to have abandoned any semblance of a “kinder, gentler” politics in its dealings with Congress. Three seemingly minor aspects of Bush's recent dealings with Congress pertaining to legislative powers suggest, if anything, a singularly aggressive effort to extend the bounds of the presidency by what I will argue is a suspect invocation of prerogative powers. The actions described below have received virtually no press attention; yet they may presage a new era of presidential expansionism exceeding that which we have witnessed to date.
Liberal Democracy as a Global Phenomenon
Authors: Fukuyama Francis
Published: May 2006

I. The Worldwide Democratic Revolution and Its Causes

It being less than ten days after the collapse of the attempted coup by communist hardliners in the Soviet Union, the coup's outcome serves as a useful reminder of the vitality that the democratic dea has for people still living under authoritarianism. The anti-communist revolution in the USSR is of course not an isolated event. The single most remarkable macropolitical phenomenon of the past generation has been the global crisis of authoritarianism, and the spread of liberal democracy in its wake, as noted by Lucian Pye in his presidential addressto this convention two years ago. By my count, there were three democracies in 1790; 13 in 1900, 27 in 1919, and 62 today.This progress has not been linear or continuous, of course: there were 14 fewer democracies in 1940 than in 1919; democracies were overthrown throughout Latin America in the 60s and 70s. Many of the countries thathave become democracies in the past few years are very unstable or of uncertain commitment to liberal values, and it would not be surprising to see a number of them lapse back into some kind of authoritarian rule in the nearfuture, as Thailand has already done this past year. Nonetheless, th trend is there. The 62 countries I countas democracies have a combined population of 2.24 billion people, or approximately 44 percent of the world's population. Moreover, neither the Soviet Union nor China are counted among the 62, and if parts or all of either country democratizes successfully, half to two-thirds of the world's population could be said to enjoy democratic rights and liberties.
America as a Model for the World? A Foreign Policy Perspective
Authors: Waltz Kenneth N.
Published: May 2006

I. How the Placement of States Affects Their Policies

Because throughout most of the years since the second World War the United States and the Soviet Union were similarly placed by their power, their external behaviors should have shown striking similarities. Did they? Yes, more than has usually been realized. The behavior of states can be compared on many counts. Their armament policies and their interventions abroad are two of the most revealing. On the former count, the United States in the early 1960s undertook the largest strategic and conventional peace-time military build-up the world has yet seen. We did so even as Khrushchev was trying at once to carry through a major reduction in the conventional forces and to follow a strategy of minimum deterrence, and we did so even though the balance of strategic weapons greatly favored the United States. As one should have expected, the Soviet Union soon followed in America's footsteps, thus restoring the symmetry of great-power behavior. And so it was through most of the years of the Cold War. Advances made by one were quickly followed by the other, with the United States almost always leading the way. Allowing for geographic differences, the overall similarity of their forces was apparent. The ground forces of the Soviet Union were stronger than those of the United States, but in naval forces the balance of advantage was reversed. The Soviet Union's largely coastal navy gradually became more of a blue-water fleet, but one of limited reach. Its navy never had more than half the tonnage of ours.
Political Economy and Militarism
Authors: Kinnucan Michael J.
Published: May 2006

Shortly after the demolition of the Berlin Wall, PS: Political Science & Politics published an article, “Socialism and Militarism,” which purported to demonstrate a positive causal relationship between socialism and militarism. Authors Thomas R. Dye and Harmon Zeigler (1989, 801) presented data and analysis leading them to conclude that “militarism is a much more pervasive characteristic of socialist nations than capitalist nations.” This finding is supportive of Payne (1989, 110) who, in Why Nations Arm stated, “the Marxist regimes are considerably more militaristic [than non-Marxist countries].”

For their examination Dye and Zeigler employed the resource allocation measures of military spending as a percentage of gross national product and the number of military personnel per 1000 population as indicators of militarism, and the classification system of Gastil (cited in Dye and Zeigler 1989) in defining national political economy types. Using this information Dye and Zeigler generated four tables that ostensibly demonstrate that socialist countries are more militaristic than capitalist countries. It is arguable, however, that Dye and Zeigler's conclusions are dubious because of the definitions and measures they have chosen to use for both socialism and militarism.
Tracking Changes in the U.S. Senate
Authors: Polsby Nelson W.
Published: May 2006

The character of the U.S. Senate has changed markedly over the last 30 years. The Senate can no longer be characterized as a well-bounded entity ruled by an “inner club” of insular grandees. Increasingly, rather, the Senate is a great forum, an echo chamber, a theater, where dramas—comedies and tragedies, soap operas and horse operas—are staged to enhance the careers of its members and to influence public policy by means of debate and public investigation.

Its special role today in the contemporary American political system is as an incubator of policy ideas and political innovations (Polsby 1984). This stands in dramatic contrast with the Senate as late as the 1950s, which was far more a body that had positioned itself as a critic and a respondent—frequently an inhospitable one—to the political innovations hatched in the executive branch and by activist presidents and forwarded to it by the House of Representatives. Thus over the last three decades the Senate has evolved from a rather negative repository of states-rights thinking, dominated by a mostly southern-led “inner club,” and hence an explicit agent of the devolved aspect of the federal system, into a predominantly nationally-oriented body.

The principal agent of this transformation has been the very great change in the life chances and therefore in the political ambitions of a large number of U.S. senators. Earlier, not so many of them entertained presidential ambitions. Today, the Senate is the main institutional source of presidential hopefuls, and for a large fraction of senators such hopes play a significant part in guiding their behavior in the Senate.