bluuebunny/crossref_metadata_2025 huggingface dataset:
On the equivalence of certain consequences of the proper forcing axiom
Authors: Nyikos Peter , Piątkiewicz Leszek
Published: May 2006

We prove that a number of axioms, each a consequence of PFA (the Proper Forcing Axiom) are equivalent. In particular we show that TOP (the Thinning-out Principle as introduced by Baumgartner in the Handbook of set-theoretic topology), is equivalent to the following statement: If I is an ideal on ω1 with ω1 generators, then there exists an uncountable X ⊆ ω1, such that either [X]ω ∩ I = ∅ or [X]ω ⊆ I.
On the basic logic ofSTITwith a single agent
Authors: Xu Ming
Published: May 2006

We present in this paper an axiomatization of Belnap and Perloff'sstittheory (a logic of “seeing to it that”) with a single agent. The idea of the proof is to apply the notion of companion sets—the same notion as used in another paper by the author that showed the decidability ofstittheory with a single agent andRefrefequivalence.
Élimination des quantificateurs dans des paires de corps
Authors: Leloup G.
Published: May 2006

On sait que par le choix d’ un langage suffisamment complexe, toute structure peut admettre une élimination des quantificateurs, malheureusement cette extension du langage peut nous éloigner des phénomènes algébriques. Nous allons nous intéresser à l’ élimination des quantificateurs pour des paires de corps. Dans le cas des paires de corps algébriquement clos et des paires denses de corps réel clos, on obtient une élimination en ajoutant au langage des prédicats ayant une signification algébrique: on peut les exprimer en disant que pour deux ensembles algébriques et donnés, il existe des points du sous-corps rationnels pour et pas pour , ou qu’ un ensemble semi-algébrique donné a des points rationnels sur le sous-corps. Robinson avait déjà abordé de façon informelle le cas des paires denses de corps réel-clos (cf. [Ro 2, p. 198]). Partant du langage des paires de corps ordonnés, enrichi de symboles de relations correspondant à l’ indépendance algébrique, il proposait d’ ajouter pas à pas des fonctions de Skolem Herbrand pour faire disparaitre les quantificateurs existentiels des formules, mais sans préciser le langage obtenu. Ici nous approchons le problème différemment en explicitant dès le départ le langage utilisé.

Grâce à ces résultats nous pourrons étudier le cas des paires séparées de corps réels clos ainsi que des paires de corps valués henseliens. En élargissant la définition d’ ensemble algébrique à tous les symboles du langage, les prédicats relationnels ajoutés ont la même signification que dans le cas des paires de corps algébriquement clos.

En comparant les techniques employées ici avec celles déjà utilisées dans [K], [B], [D 1] et [L], on remarque qu’il est possible de traîter une grande partie de l’ étude (complétude, modèle complétude, élimination des quantificateurs) des paires de corps algébriquement clos, réel-clos ou henseliens en se basant sur des prolongements d’ isomorphismes entre sous-structures dénombrables où l’ une des deux est contenue dans une structure ω1-saturée.
Embeddability and the word problem
Authors: Dekov Deko V.
Published: May 2006

Let be a finitely presented variety with operations Ω and let be the variety having the same set of operations Ω but defined by the empty set of identities. A partial-algebra is a set P with a set of mappings containing for each n-ary operation f of Ω a mapping , where D ⊆ Pn. An incomplete -algebra is a partial -algebra which satisfies the defining identities of , insofar as they can be applied to the partial operations of (Trevor Evans [4, p. 67]). We call an incomplete -algebra a partial Evans-algebra if it can be embedded in a member of the variety .

If the class of all partial Evans -algebras is (first-order) finitely axiomatizable, then the word problem for the variety is solvable. (Evans [4, 5]). In 1953 Evans [5, p. 79] raised the question of whether the converse is true. In this paper we show that the answer is in the negative.

Let CSg denote the variety of commutative semigroups. We call an incomplete CSg-algebra an incomplete commutative semigroup and we call a partial Evans CSg-algebra a partial Evans commutative semigroup. It is known (A. I. Malcev [9] see also Evans [6]) that the variety of commutative semigroups has solvable word problem. We show (Theorem 1) that the class of all partial Evans commutative semigroups is not finitely axiomatizable. Therefore the solvability of the word problem for the variety of commutative semigroups does not imply finite axiomatizability of the class of all partial Evans commutative semigroups.
A small reflection principle for bounded arithmetic
Authors: Verbrugge Rineke , Visser Albert
Published: May 2006

We investigate the theory IΔ0+Ω1 and strengthen [Bu86, Theorem 8.6] to the following: if NP ≠ co-NP, then Σ-completeness for witness comparison foumulas is not provable in bounded arithmetic. i.e.,

Next we study a “small reflection principle” in bounded arithmetic. We prove that for all sentences φ

The proof hinges on the use of definable cuts and partial satisfaction predicates akin to those introduced by Pudlák in [Pu86].

Finally, we give some applications of the small reflection principle, showing that the principle can sometimes be invoked in order to circumvent the use of provable Σ-completeness for witness comparison formulas.
A logic for approximate reasoning
Authors: Ying Mingsheng
Published: May 2006

Classical logic is not adequate to face the essential vagueness of human reasoning, which is approximate rather than precise in nature. The logical treatment of the concepts of vagueness and approximation is of increasing importance in artificial intelligence and related research. Consequently, many logicians have proposed different systems of many-valued logic as a formalization of approximate reasoning (see, for example, Goguen [G], Gerla and Tortora [GT], Novak [No], Pavelka [P], and Takeuti and Titani [TT]). As far as we know, all the proposals are obtained by extending the range of truth values of propositions. In these logical systems reasoning is still exact and to make a conclusion the antecedent clause of its rule must match its premise exactly. In addition. Wang [W] pointed out: “If we compare calculation with proving,... Procedures of calculation... can be made so by fairly well-developed methods of approximation; whereas... we do not have a clear conception of approximate methods in theorem proving.... The concept of approximate proofs, though undeniably of another kind than approximations in numerical calculations, is not incapable of more exact formulation in terms of, say, sketches of and gradual improvements toward a correct proof” (see pp, 224–225). As far as the author is aware, however, no attempts have been made to give a conception of approximate methods in theorem proving.

The purpose of this paper is. unlike all the previous proposals, to develop a propositional calculus, a predicate calculus in which the truth values of propositions are still true or false exactly and in which the reasoning may be approximate and allow the antecedent clause of a rule to match its premise only approximately. In a forthcoming paper we shall establish set theory, based on the logic introduced here, in which there are ∣L∣ binary predicates ∈λ, λ ∈ L such that R(∈, ∈λ) = λ where ∈ stands for ∈1 and 1 is the greatest element in L, and x ∈λy is interpreted as that x belongs to y in the degree of λ, and relate it to intuitionistic fuzzy set theory of Takeuti and Titani [TT] and intuitionistic modal set theory of Lano [L]. In another forthcoming paper we shall introduce the resolution principle under approximate match and illustrate its applications in production systems of artificial intelligence.
Frege's theorem in a constructive setting
Authors: Bell John L.
Published: May 2006

By Frege's Theorem is meant the result, implicit in Frege's Grundlagen, that, for any set E, if there exists a map υ from the power set of E to E satisfying the condition

then E has a subset which is the domain of a model of Peano's axioms for the natural numbers. (This result is proved explicitly, using classical reasoning, in Section 3 of [1].) My purpose in this note is to strengthen this result in two directions: first, the premise will be weakened so as to require only that the map υ be defined on the family of (Kuratowski) finite subsets of the set E, and secondly, the argument will be constructive, i.e., will involve no use of the law of excluded middle. To be precise, we will prove, in constructive (or intuitionistic) set theory, the following

Theorem. Let υ be a map with domain a family of subsets of a set E to E satisfying the following conditions:

(i) ø ϵdom(υ)

(ii)∀U ϵdom(υ)∀x ϵ E − UU ∪ x ϵdom(υ)

(iii)∀UV ϵdom(5) υ(U) = υ(V) ⇔ U ≈ V.

Then we can define a subset N of E which is the domain of a model of Peano's axioms.
Invisible genericity and 0#
Authors: Stanley M. C.
Published: May 2006

0# can be invisibly class generic.
Gödel sentences of bounded arithmetic
Authors: Takeuti Gaisi
Published: May 2006

In [1], S. Buss introduced the systems of Bounded Arithmetic for (i = 0,1,2,…) which has a close relationship to classes in polynomial hierarchy.

In [4], we defined a very special kind of proof-predicate Prfi for which gives detailed information on bounds of free variables used in the proof. There we also introduced infinitely many Gödel sentences for Prfi (k = 0, 1, 2, …) and showed that the properties of Prfi and are closely related to the P ≠ NP problem. Then we presented many conjectures on Prfi and which imply P ≠ NP.

Now in [2], Feferman emphasized that the arithmetization of metamathematics must be carried out intensionally. Bounded Arithmetic is a very interesting case in this sense.

In this paper, we also introduce the usual proof-predicate PRFi for and infinitely many Gödel sentences for PRFi(k= 0, 1, 2, …). Then we show that (Prfi, )and (PRFi, ) form a good contrast, this contrast is also closely related to the P ≠ NP problem, and present more conjectures which imply P ≠ NP.

As in [4] we define to be the following extension of Buss' original .

(1) We add finitely many function symbols which express polynomial time computable functions to Buss' original language of .

(2) All basic axioms on function symbols and ≤ can be expressed by initial sequents without logical symbols.
Variations on a theme by Weiermann
Authors: Arai Toshiyasu
Published: May 2006

Weiermann [18] introduces a new method to generate fast growing functions in order to get an elegant and perspicuous proof of a bounding theorem for provably total recursive functions in a formal theory, e.g., in PA. His fast growing function θαη is described as follows. For each ordinal a and natural number n let denote a finitely branching, primitive recursive tree of ordinals, i.e., an ordinal as a label is attached to each node in the tree so that the labelling is compatible with the tree ordering. Then the tree is well founded and hence finite by König's lemma. Define θαηn =the depth of the tree =the length of the longest branch in .

We introduce new fast and slow growing functions in this mode of definitions and show that each of these majorizes provably total recursive functions in PA.
Normal monomodal logics can simulate all others
Authors: Kracht Marcus , Wolter Frank
Published: May 2006

This paper shows that non-normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic.
Quine's ‘limits of decision’
Authors: Purdy William C.
Published: May 2006

In a 1969 paper, Quine coined the term ‘limits of decision”. This term evidently refers to limits on the logical vocabulary of a logic, beyond which satisfiability is no longer decidable. In the same paper, Quine showed that not only monadic formulas, but homogeneous k -adic formulas for arbitrary k lie on the decidable side of the limits of decision. But the precise location of the limits of decision has remained an open question. The present paper answers that question. It addresses the question of decidability of those sublogics of first-order logic that are defined in terms of their logical vocabularies. A complete answer is obtained, thus locating exactly Quine's limits of decision.
A Note on a-Prime Models
Authors: Hart Bradd , Sokolović Željko , Tanovic Predrag
Published: May 2006

We answer a question of Cassidy and Kolchin about the universality of the constrained closure of a differential field by working in a larger category of models.
Amalgamation in relation algebras
Authors: Marx Maarten
Published: May 2006

We investigate amalgamation properties of relational type algebras. Besides purely algebraic interest, amalgamation in a class of algebras is important because it leads to interpolation results for the logic corresponding to that class (cf. [15]). The multi-modal logic corresponding to relational type algebras became known under the name of “arrow logic” (cf. [18, 17]), and has been studied rather extensively lately (cf. [10]). Our research was inspired by the following result of Andréka et al. [1].

Let K be a class of relational type algebras such that

(i) composition is associative,

(ii) K is a class of boolean algebras with operators, and

(iii) K contains the representable relation algebras RRA.

Then the equational theory of K is undecidable.

On the other hand, there are several classes of relational type algebras (e.g., NA, WA denned below) whose equational (even universal) theories are decidable (cf. [13]). Composition is not associative in these classes. Theorem 5 indicates that also with respect to amalgamation (a very weak form of) associativity forms a borderline. We first recall the relevant definitions.
Fibring: completeness preservation
Authors: Zanardo Alberto , Sernadas Amilcar , Sernadas Cristina
Published: May 2006

A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. An example is provided showing that completeness is not always preserved by fibring ligics endowed with standard (non general) semantics. A categorial characterization of fibring is provided using coproducts and cocartesian liftings.
Monoid based semantics for linear formulas
Authors: Mitchell W. P. R. , Simmons H.
Published: May 2006

Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of handling duality.
Realization of analysis into Explicit Mathematics
Authors: Tupailo Sergei
Published: May 2006

We define a novel interpretation of second order arithmetic into Explicit Mathematics. As a difference from standard -interpretation, which was used before and was shown to interpret only subsystems proof-theoretically weaker than T0. our interpretation can reach the full strength of T0. The -interpretation is an adaptation of Kleene's recursive readability, and is applicable only to intuitionistic theories.
Self-verifying axiom systems, the incompleteness theorem and related reflection principles
Authors: Willard Dan E.
Published: May 2006

We will study several weak axiom systems that use the Subtraction and Division primitives (rather than Addition and Multiplication) to formally encode the theorems of Arithmetic. Provided such axiom systems do not recognize Multiplication as a total function, we will show that it is feasible for them to verify their Semantic Tableaux, Herbrand, and Cut-Free consistencies. If our axiom systems additionally do not recognize Addition as a total function, they will be capable of recognizing the consistency of their Hilbert-style deductive proofs. Our axiom systems will not be strong enough to recognize their Canonical Reflection principle, but they will be capable of recognizing an approximation of it, called the “Tangibility Reflection Principle”. We will also prove some new versions of the Second Incompleteness Theorem stating essentially that it is not possible to extend our exceptions to the Incompleteness Theorem much further.
Logics of belief change without linearity
Authors: Cantwell John
Published: May 2006

Ever since [4]. systems of spheres have been considered to give an intuitive and elegant way to give a semantics for logics of theory- or belief- change. Several authors [5, 11] have considered giving up the rather strong assumption that systems of spheres be linearly ordered by inclusion. These more general structures are calledhypertheoriesafter [8]. It is shown that none of the proposed logics induced by these weaker structures are compact and thus cannot be given a strongly complete axiomatization in a finitary logic. Complete infinitary axiomatizations are given for several intuitive logics based on hypertheories that are not linearly ordered by inclusion.
Minimal fields
Authors: Wagner Frank O.
Published: May 2006

A minimal field of non-zero characteristic is algebraically closed.
A note on the isomorphism problem for SK[G]
Authors: Chatzidakis Zoé , Pappas Peter
Published: May 2006

Let G be an infinite abelian p-group and let K be a field of characteristic ≠ p. Let K[G] be the set of all sums Σg∈Gagg where the ag are in K, and all but finitely many ag are 0. Then K[G] is a K-algebra, with multiplication induced by the group multiplication on G.

If G is countable, then the isomorphism type of K[G] has been completely described by S. D. Berman [1]. If G is a direct sum of countable groups, one can also describe K[G], as K[⊕iGi] ≃ ⊗iK[Gi]. If K contains all pn-th roots of unity, then K[G] is isomorphic to the ring of continuous functions from a Boolean space X to the field K with the discrete topology. In that case, the group UK[G] of invertible elements of K[G] is isomorphic to the direct sum of ∣G∣ copies of K×. More generally, if K is of the second kind with respect to p (see below for the definition), the group UK[G] has a simple description.

Consider the subgroup SK[G] of elements Σgagg which have order a power of p and such that Σg ag = 1. This group is of course much simpler than UK[G]. Classifying SK[G] up to isomorphism reduces to the case where G has no element of infinite height, see [7]. If G is a direct sum of cyclic groups then the isomorphism type of SK[G] has been completely determined, in [2, 3, 7, 8]. The aim of this note is to show that a similar result is in general not possible for uncountable G. We use an invariant Γ associated to abelian groups, and for any regular uncountable cardinal κ, exhibit 2κ groups G for which Γ(G) = Γ(SK[G]) are pairwise distinct. Our work is based on a construction of Shelah [9], who constructed 2κ non-isomorphic abelian p-groups of cardinality κ for κ an uncountable regular cardinal.
Minimality and completions of PA
Authors: Knight Julia F.
Published: May 2006

The results in this paper say that natural upper bounds for sets of degrees associated with theories and models of arithmetic cannot be minimal. The basic new result says that for any completion T of PA, there is another completion S such that S<TT and Rep(S) = Rep(T). This immediately implies that deg(T) is not minimal over {deg(X): X ∈ Rep(T)}. As an application of the basic result, we obtain the fact that if is a non-standard model of TA (true arithmetic), then deg () cannot be minimal over {deg(X): X is arithmetical}. More generally, if is a non-standard model of an arbitrary completion T of PA, then deg() cannot be minimal over {deg(): X ∈ Rep(T)}. We vary the basic result, making S′ ≡TT′. As an application of the variant, we obtain the fact that if is a non-standard model of PA, then {deg(): ≅ } has no minimal element.

The remainder of the present section gives a brief account of the background needed for the basic new result and the variant. These two results are proved in Section 2. The applications are given in Section 3, along with further background needed for the applications. One important source of ideas used in the present paper is a paper of Scott [9]. In addition, there are ideas taken from Tennenbaum [12], Feferman [3], Marker [6], [7], and Solovay. Chapter 19 of [1] gathers together most of this material. In fact, it contains all that is really essential. In one application, we appeal to Solovay's result on degrees of models of an arbitrary completion of PA, a result which is not completely proved in [1]. However, for the best application, which implies all the others, we use only some ideas from the proof of Solovay's theorem. These are given in lemmas that are proved in Section 3, where they are needed, or taken from [1], While the proof of Solovay's result requires an infinitely nested priority construction, our best application rests on nothing more than finite-injury constructions.
Policy, Institutions, and Coalition Avoidance: Norwegian Governments, 1945–1990
Authors: Strøm Kaare , Leipart Jørn Y.
Published: May 2006

Norwegian party politics is characterized by coalition avoidance that defies conventional coalition theory. This failure of coalescence can be caused either by policy pursuit (preference-induced) or by institutional constraint (structure-induced). We test the explanatory power of policy-based and institutional explanations, relying on content analysis of authoritative party and government documents for our policy measures. The results show that the left–right policy dimension has powerfully constrained Norwegian interparty bargaining and that policy-based coalition theory can account for many apparent anomalies in Norwegian coalition politics. A permissive institutional environment has also fostered coalition avoidance. Although core-based coalition theory can thus be successfully adapted to the Norwegian case, it rests on a number of critical assumptions that limit its general applicability.
Utility, Property, and Political Participation: James Mill on Democratic Reform
Authors: Stimson Shannon C. , Milgate Murray
Published: May 2006

On the philosophical plane, James Mill's political thinking began from a model of man quintessentially utilitarian in constitution. Starting with individual agents, it was to his account of the science of human nature that he turned in the quest for a science of politics suitable for the modern world. If James Mill's science of politics was individualist in character, it was neither automatically nor necessarily democratic in the practical political arena. On that subject, everything turned on the question of judging when (or if) individual capacity had reached an acceptable standard. This criterion proved to be sufficiently malleable to allow him to appear either expansive and democratic or narrow and elitist, as the case required.
Socrates' Aspasian Oration: The Play of Philosophy and Politics in Plato'sMenexenus
Authors: Salkever Stephen G.
Published: May 2006

Plato'sMenexenusis overlooked, perhaps because of the difficulty of gauging its irony. In it, Socrates recites a funeral oration he says he learned from Aspasia, describing events that occurred after the deaths of both Socrates and Pericles' mistress. But the dialogue's ironic complexity is one reason it is a central part of Plato's political philosophy. In both style and substance,Menexenusrejects the heroic account of Athenian democracy proposed by Thucydides' Pericles, separating Athenian citizenship from the quest for immortal glory; its picture of the relationship of philosopher to polis illustrates Plato's conception of the truepolitikosin theStatesman. In both dialogues, philosophic response to politics is neither direct rule nor apolitical withdrawal.Menexenuspresents a Socrates who influences politics indirectly, by recasting Athenian history and thus transforming the terms in which its political alternatives are conceived.
Jugoslavia in the Making
Authors: Armstrong Hamilton Fish
Published: May 2006

Both Serbs and Croats have deserved more conciliatory and understanding leadership than they have received since the war. History had treated them very differently, and once they were united in a Jugoslav national state every resource of statesmanship should have been exercised to ease over their psychological and material dissimilarities. Writers have made much of the religious gap between Catholic Croats and Orthodox Serbs, and of the former's use of the Latin alphabet and the latter's of the Cryillic. The fact remains that they are of the same race, speak the same language, and for generations dreamed of union and worked for it.
Politics and the Environment: Nonlinear Instabilities Dominate
Authors: Brown Courtney
Published: May 2006

This analysis investigates a formal nonlinear systems model characterizing longitudinal change in the environment as a function of oscillating partisan control of the White House. It is assumed that one political party will tend to favor help for the environment despite some economic costs, whereas the other party will generally favor economic growth over environmental concerns. These policy changes affect the environment interactively with both public concern for particular environmental problems and the economic costs relating to environmental repair. This interaction with policy changes causes a disruption in the continuously evolving balance between the social factors that damage the environment and the environment's own ability to recover. The disruptive potential to the environment is considerably ameliorated with a reduction in the electoral cycling.
Power and Influence in State Legislative Policymaking: The Interaction of Gender and Position in Committee Hearing Debates
Authors: Kathlene Lyn
Published: May 2006

There is an implicit assumption behind advocating for more minorities or women in elected office, namely, that these officials will bring a new power and influence to their underrepresented groups. However, for women, this idealized viewpoint ignores the social dynamics that subordinate women's words and actions even in “well-balanced” male and female group interactions. Using transcribed verbatim transcripts of 12 state legislative committee hearings, this research analyzes the conversational dynamics of committee members, witnesses, chairs, and sponsors. Sex differences among committee members are highly significant, even after accounting for political factors and structural features of the hearing. In addition, male and female chairs do not conduct hearings in the same way, and these differences affect the behavior of witnesses and committee members. The findings suggest that as the proportion of women increases in a legislative body, men become more verbally aggressive and controlling of the hearing. Women legislators may be seriously disadvantaged and unable to participate equally in legislative policymaking in committee hearings.
Note on Słupecki T-functions
Authors: Clay Robert E.
Published: May 2006

For the m-valued (2<w<∞) logics of Łukasiewicz as described in [2] using the values 1,2, …, m and based on the functions f(p, q) = max(1,q—p+1) and g(p) = m—p+1, Evans and Schwartz have essentially2 proved in [1] that the addition of a constant function i, 1<i<m, yields functional completeness if and only if (m—1, i—1)= 1.3 In this note it will be shown that if n constant functions i1, …, in, 1<ik<m and 1≦k≦n, are added, functional completeness obtains if and only if (m—1, i1—1, …, in—1) = 1.
Simplified axioms for many-valued quantification theory
Authors: Turquette Atwell R.
Published: May 2006

The basic aim of the present paper is to simplify the axioms for many-valued quantification theory which were developed by Rosser and Turquette in Many-valued logics ([10], pp. 33–34 and pp. 63–64). The simplification which is achieved results not only from a reduction in the number of axiom schemes and rules of inference, but also by obtaining greater formal similarity to some elegant axioms for standard 2-valued quantification theory. This result will not be accomplished by establishing the formal interdeducibility between our simplified axioms and the Rosser-Turquette set. On the contrary, it will be shown that these two sets of axioms are not formally interdeducible.

What will be shown is that whenever the Rosser-Turquette axioms are used to define a plausible set of statements, this set of statements can be defined using our simplified axioms. The exact meaning of “plausible” will become clear from what follows, so for the moment it will be sufficient to remark that a set of statements is plausible if and only if each statement of the set is analytic in the sense that the statements take designated truth-values exclusively. In general, a Rosser-Turquette set of axioms would be used to define a set of plausible statements, and in such a case our simplified axioms could be used to achieve the same result.
Mathematical significance of consistency proofs
Authors: Kreisel G.
Published: May 2006

The principal aim of the present paper is to sketch some mathematical applications of the work of the Hilbert school in the foundations of mathematics. Most of them depend on theε-theorems of Hilbert-Bernays II [6], or of Ackermann [1], but instead the work of Gentzen [5] or Schütte [25], which does not use theε-symbol, could have been applied.

The avowed purpose of all this work is described in the introduction to volume I of Hilbert-Bernays: the consistency of the usual principles of proof is to be established by means of finitist methods, or at least, by means of methods which are more “evident” or more “constructive” than the principles under discussion. This formulation seems to have several defects:

(1) Since the notion of constructive proof is vague, the whole formulation of the program is vague; and though an exact formulation constitutes, of course, an interesting problem for the logician, because of this vagueness the mathematician does not find the program attractive.

(2) The formulation does not cover too well the actual substance of the material contained in [6]; e.g. theε-theorems for the predicate calculus go far beyond establishing mere consistency of the predicate calculus. It is significant that it is precisely these theorems which lead to the more interesting applications, e.g. the use of theε-theoremswithequality in the solution of Hilbert's 17th problem given below.
The classical and the ω-complete arithmetic
Authors: Grzegorczyk A. , Mostowski A. , Ryll-Nardzewski C.
Published: May 2006

We consider two formal systems for the theory of (natural) numbers, both of which are applied second-order functional calculi with equality and the description operator. The two systems have the same primitive symbols, rules of formation, and axioms, differing only in the rules of inference.

The primitive logical symbols of the systems are the improper symbols (,), the prepositional connectives ∨, &, ⊃, ≡, ~, the quantifiers ( ), (E), the equality symbol =, the description operator ι,-infinitely many distinct individual (or number) variables, and for each positive integer k infinitely many distinct k-place function variables. Our systems have in addition the following four primitive nonlogical (or arithmetical) constants:0, 1, +, ×.

The classes of “number formulas” (nfs) and “propositional formulas” (pfs) are defined inductively as the least classes of formal expressions (i.e. of concatenations of primitive symbols) satisfying the following conditions:

(1) 0, 1, and the number variables are nfs.
Extensions of some theorems of Anderson and Belnap
Authors: Rose Alan
Published: May 2006

The object of this note is to extend to Post's m-valued propositional calculus1 the axiomatization by Anderson and Belnap2 of the 2-valued propositional calculus.

Notation and definitions. We shall use the symbols ∼ and v for the primitives of Post and shall otherwise, except as stated below, use the same notation and definitions as in the previous paper.
An extension of a theorem of margaris
Authors: Rose Alan
Published: May 2006

Margaris has shown1 that for every triple 〈s,t,m〉 of integers such that 1 ≦ s < t < m it is possible to construct a formalisation of an m-valued propositional calculus satisfying the following conditions: I. Every statement which takes only truth-values belonging to the set {1, …,s} is provable. II. Every provable statement takes only truth-values belonging to the set {1, …, t}. III. There exist statements Pk, Qk which take only truth-values belonging to the set {1, …, k) and neither of which takes only truth-values belonging to the set {1, …, k—1} such that Pk is provable and Qk is unprovable (k = s+1, …, t). The systems of Margaris are all functionally incomplete and he appears to suggest2 that it is impossible to construct functionally complete systems having the required properties.
An unsolvable problem in number theory
Authors: Putnam Hilary
Published: May 2006

This paper presents several results whose common element is their connection with Hubert's tenth problem.1 The one that seems most striking (perhaps because it can be stated with a minimum of technical apparatus) is this: there does not exist an algorithm for determining whether or not a polynomial (in n variables) represents every integer.2

In addition, the present paper (i) gives a simple characterization of the diophantine sets (of positive, non-negative, and arbitrary integers), and (ii) gives a rigorous proof of Myhill's theorem [6] that there is no decision method for statements of the form
On the influence of stratospheric water vapor changes on the tropospheric circulation
Authors: Joshi Manoj M. , Charlton Andrew J. , Scaife Adam A.
Published: May 2006

Observations suggest that the mixing ratio of water vapour in the stratosphere has increased by 20–50% between the 1960s and mid‐1990s. Here we show that inclusion of such a stratospheric water vapour (SWV) increase in a state‐of‐the‐art climate model modifies the circulation of the extratropical troposphere: the modeled increase in the North Atlantic Oscillation (NAO) index is 40% of the observed increase in NAO index between 1965 and 1995, suggesting that if the SWV trend is real, it explains a significant fraction of the observed NAO trend. Our results imply that SWV changes provide a novel mechanism for communicating the effects of large tropical volcanic eruptions and ENSO events to the extratropical troposphere over timescales of a few years, which provides a mechanism for interannual climate predictability. Finally, we discuss our results in the context of regional climate change associated with changes in methane emissions.
Variational approach to the volume viscosity of fluids
Authors: Zuckerwar Allan J. , Ash Robert L.
Published: May 2006

The variational principle of Hamilton is applied to develop an analytical formulation to describe the volume viscosity in fluids. The procedure described here differs from those used in the past in that a dissipative process is represented by the chemical affinity and progress variable (sometimes called “order parameter”) of a reacting species. These state variables appear in the variational integral in two places: first, in the expression for the internal energy, and second, in a subsidiary condition accounting for the conservation of the reacting species. As a result of the variational procedure, two dissipative terms appear in the Navier-Stokes equation. The first is the traditional volume viscosity term, proportional to the dilatational component of velocity; the second term is proportional to the material time derivative of the pressure gradient. Values of the respective volume viscosity coefficients are determined by applying the resulting volume-viscous Navier-Stokes equation to the case of acoustical propagation and then comparing expressions for the dispersion and absorption of sound. The formulation includes the special case of equilibration of the translational degrees of freedom. As examples, values are tabulated for dry and humid air, argon, and sea water.
Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration
Authors: Tirtaatmadja V. , McKinley G. H. , Cooper-White J. J.
Published: May 2006

The dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behavior that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localized increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur in the equivalent Newtonian fluid. Alternatively, a cylindrical filament forms in which elastic stresses and capillary pressure balance, and the radius decreases exponentially with time. A (0+1)-dimensional finitely extensible nonlinear elastic dumbbell theory incorporating inertial, capillary, and elastic stresses is able to capture the basic features of the experimental observations. Before the critical “pinch time” tp, an inertial-capillary balance leads to the expected 2∕3-power scaling of the minimum radius with time: Rmin∼(tp−t)2∕3. However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elastocapillary balance for times t>tp. In this region, the filament radius decreases exponentially with time Rmin∼exp[(tp−t)∕λ1], where λ1 is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of polyethylene oxide solutions of varying concentrations and molecular weights obtained from high speed imaging of the rate of change of filament radius are significantly higher than the relaxation times estimated from Rouse-Zimm theory, even though the solutions are within the dilute concentration region as determined using intrinsic viscosity measurements. The effective relaxation times exhibit the expected scaling with molecular weight but with an additional dependence on the concentration of the polymer in solution. This is consistent with the expectation that the polymer molecules are in fact highly extended during the approach to the pinch region (i.e., prior to the elastocapillary filament thinning regime) and subsequently as the filament is formed they are further extended by filament stretching at a constant rate until full extension of the polymer coil is achieved. In this highly extended state, intermolecular interactions become significant, producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions.
Aeolian tones radiated from flow past two square cylinders in a side-by-side arrangement
Authors: Inoue O. , Iwakami W. , Hatakeyama N.
Published: May 2006

The sound generated by two square cylinders placed in a side-by-side arrangement in a uniform flow at low Mach numbers is studied by direct solution of the two-dimensional unsteady compressible Navier-Stokes equations. Special attention is paid to the effect of the spacing between the two cylinders on the generation mechanism of the sound. Results show that sound pressure fields as well as flow fields show different features depending on the spacing; six different wake patterns (nonsynchronized, antiphase and in-phase synchronized, flip-flopping, single bluff-body, and steady patterns) are observed and, depending on the wake pattern, sound pressure fields also show different features. Two types of bifurcation phenomenon are observed where two different wake patterns exist for the same spacing and either of the two patterns appears depending on an initial condition; different sound pressure fields appear in response to the wake patterns. Results also show that Curle's dipole solution does not predict well the direct numerical simulation results in the antiphase-synchronized pattern at a small spacing and the flip-flopping pattern, but that it gives a good approximation in the nonsynchronized, in-phase-synchronized, and single-bluff-body patterns.
Oscillatory convective structures and solutal jets originated from discrete distributions of droplets in organic alloys with a miscibility gap
Authors: Lappa Marcello
Published: May 2006

The pattern formation process driven by N droplets out of thermodynamic equilibrium, uniformly distributed on the bottom of a container filled with a partially miscible organic liquid, is investigated for different values of N by means of a multiprocessor solution of the Navier-Stokes equations. The considered system is intended to model the typical phenomena occurring during the thermal processing of liquid-liquid systems exhibiting a miscibility gap (the so-called “immiscible alloys”). These alloys undergo sedimentation of the separated heavier phase to the bottom of the container under normal gravity conditions. Droplets in nonequilibrium conditions are responsible for the occurrence of still poorly known fluid-dynamic instabilities. In the present analysis we provide a clear and quite exhaustive picture of the different stages of evolution of fluid motion inside the container. The distribution of solute is found to depend on the complex multicellular structure of the convective field and on associated “pluming phenomena.” Significant adjustments in the pattern take place as time passes. The structure of the velocity field and the number of rising solutal plumes exhibit sensitivity to the number of droplets and to the possible presence of surface Marangoni effects. New classes of possible instability mechanisms (pulsating, traveling, erratic) are identified and described. The investigation provides “local” details as well as general rules and trends about the macroscopic evolution (i.e., “ensemble behaviors”) of the system.
A Novel Lipoxygenase in Pea Roots. Its Function in Wounding and Biotic Stress
Authors: Veronico Pasqua , Giannino Donato , Melillo M. Teresa , Leone Antonella , Reyes Aurelio , Kennedy Malcolm W. , Bleve-Zacheo Teresa
Published: May 2006

The genome of pea (Pisum sativum) contains genes encoding a family of distinct lipoxygenases (LOX). Among these, LOXN2 showed eight exons encoding a 93.7-kD enzyme, harboring two C-terminal deletions and an unusual arginine/threonine-tyrosine motif in the domain considered to control the substrate specificity. LOXN2, when overexpressed in yeast, exhibited normal enzyme activity with an optimum at pH 4.5, and a dual positional specificity by releasing a 3:1 ratio of C-9 and C-13 oxidized products. The predicted LOXN2 structure lacked a loop present in soybean (Glycine max) LOX1, in a position consistent with control of the degree of substrate access to the catalytic site and for LOXN2's dual positional specificity. The LOXN2 gene was tightly conserved in the Progress 9 and MG103738 genotypes, respectively, susceptible and resistant to the root cyst nematode Heterodera goettingiana. LOXN2 transcription was monitored in roots after mechanical injury and during nematode infection. The message peaked at 3 and 24 h after wounding in both genotypes and was more abundant in the resistant than in the susceptible pea. In nematode-infected roots, transcription of several LOX genes was triggered except LOXN2, which was repressed in both genotypes. In situ hybridization revealed that LOXN2 message was widespread in the cortex and endodermis of healthy roots, but specifically localized at high level in the cells bordering the nematode-induced syncytia of infected roots. However, LOXN2 transcript signal was particularly intense in collapsing syncytia of MG103738 roots, suggesting LOXN2 involvement in late mechanisms of host resistance.
Rapid vasoregulatory mechanisms in exercising human skeletal muscle: dynamic response to repeated changes in contraction intensity
Authors: Rogers Anna M. , Saunders Natasha R. , Pyke Kyra E. , Tschakovsky Michael E.
Published: May 2006

We tested the hypothesis that vasoregulatory mechanisms exist in humans that can rapidly adjust muscle blood flow to repeated increases and decreases in exercise intensity. Six men and seven women (age, 24.4 ± 1.3 yr) performed continuous dynamic forearm handgrip contractions (1- to 2-s contraction-to-relaxation duty cycle) during repeated step increases and decreases in contraction intensity. Three step change oscillation protocols were examined: Slow (7 contractions per contraction intensity × 10 steps); Fast (2 contractions per contraction intensity × 15 steps); and Very Fast (1 contraction per contraction intensity × 15 steps). Forearm blood flow (FBF; Doppler and echo ultrasonography), heart rate (ECG), and mean arterial pressure (arterial tonometry) were examined for the equivalent of a cardiac cycle during each relaxation phase (FBFrelax). Mean arterial pressure and heart rate did not change during repeated step changes ( P = 0.352 and P = 0.190). For both Slow and Fast conditions, relaxation phase FBFrelaxadjusted immediately and repeatedly to both increases and decreases in contraction intensity, and the magnitude and time course of FBFrelaxchanges were virtually identical. For the Very Fast condition, FBFrelaxincreased with the first contraction and thereafter slowly increased over the course of repeated contraction intensity oscillations. We conclude that vasoregulatory mechanisms exist in human skeletal muscle that are capable of rapidly and repeatedly adjusting muscle blood flow with ongoing step changes in contraction intensity. Importantly, they demonstrate symmetry in response magnitude and time course with increasing versus decreasing contraction intensity but cannot adjust to very fast exercise intensity oscillations.
Constitutional Law in 1921–1922: The Constitutional Decisions of the Supreme Court of the United States in the October Term, 1921
Authors: Corwin Edward S.
Published: May 2006

The central point of interest in the work of the court the past term is supplied by the large attention given to the question of the rights and duties of labor under the law. The problem is approached repeatedly, both from the side of the state's police power and that of national power, and in the field of statutory as well as that of constitutional construction. Important results were also reached in interpretation of the “commerce” clause, both in its aspect as a source of national power and in its aspect—because of the doctrine of the exclusiveness of the power of Congress—as a restriction on the states; but especially in the latter aspect. However, the most interesting single decision of the term for students of constitutional theory and of government was one dealing with the national power of taxation.