bluuebunny/crossref_metadata_2025 huggingface dataset:
Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic
Authors: Abrusci V. Michele
Published: May 2006

The linear logic introduced in [3] by J.-Y. Girard keeps one of the so-called structural rules of the sequent calculus: the exchange rule. In a one-sided sequent calculus this rule can be formulated as

The exchange rule allows one to disregard the order of the assumptions and the order of the conclusions of a proof, and this means, when the proof corresponds to a logically correct program, to disregard the order in which the inputs and the outputs occur in a program.

In the linear logic introduced in [3], the exchange rule allows one to prove the commutativity of the multiplicative connectives, conjunction (⊗) and disjunction (⅋). Due to the presence of the exchange rule in linear logic, in the phase semantics for linear logic one starts with a commutative monoid. So, the usual linear logic may be called commutative linear logic.

The aim of the investigations underlying this paper was to see, first, what happens when we remove the exchange rule from the sequent calculus for the linear propositional logic at all, and then, how to recover the strength of the exchange rule by means of exponential connectives (in the same way as by means of the exponential connectives ! and ? we recover the strength of the weakening and contraction rules).
Louveau's theorem for the descriptive set theory of internal sets
Authors: Schilling Kenneth , Živaljević Boško
Published: May 2006

We give positive answers to two open questions from [15]. (1) For every set C countably determined over , if C is then it must be over , and (2) every Borel subset of the product of two internal sets X and Y all of whose vertical sections are can be represented as an intersection (union) of Borel sets with vertical sections of lower Borel rank. We in fact show that (2) is a consequence of the analogous result in the case when X is a measurable space and Y a complete separable metric space (Polish space) which was proved by A. Louveau and that (1) is equivalent to the property shared by the inverse standard part map in Polish spaces of preserving almost all levels of the Borel hierarchy.
Peano arithmetic may not be interpretable in the monadic theory of linear orders
Authors: Lifsches Shmuel , Shelah Saharon
Published: May 2006

Gurevich and Shelah have shown that Peano Arithmetic cannot be interpreted in the monadic second-order theory of short chains (hence, in the monadic second-order theory of the real line). We will show here that it is consistent that the monadic second-order theory of no chain interprets Peano Arithmetic.
Adding one random real
Authors: Bartoszyński Tomek , Rosłanowski Andrzej , Shelah Saharon
Published: May 2006

We study the cardinal invariants of measure and category after adding one random real. In particular, we show that the number of measure zero subsets of the plane which are necessary to cover graphs of all continuous functions may be large while the covering for measure is small.
A sufficient condition for completability of partial combinatory algebras
Authors: Asperti Andrea , Ciabattoni Agata
Published: May 2006

A Partial Combinatory Algebra is completable if it can be extended to a total one. In [1] it is asked (question 11, posed by D. Scott, H. Barendregt, and G. Mitschke) if every PCA can be completed. A negative answer to this question was given by Klop in [12, 11]; moreover he provided a sufficient condition for completability of a PCA (M, •, K,S) in the form of ten axioms (inequalities) on terms of M. We prove that just one of these axiom (the so called Barendregt's axiom) is sufficient to guarantee (a slightly weaker notion of) completability.
Stretchings
Authors: Finkel O. , Ressayre J. P.
Published: May 2006

A structure is locally finite if every finitely generated substructure is finite; local sentences are universal sentences all models of which are locally finite. The stretching theorem for local sentences expresses a remarkable reflection phenomenon between the finite and the infinite models of local sentences. This result in part requires strong axioms to be proved; it was studied by the second named author, in a paper of this Journal, volume 53. Here we correct and extend this paper; in particular we show that the stretching theorem implies the existence of inaccessible cardinals, and has precisely the consistency strength of Mahlo cardinals of finite order. And we present a sequel due to the first named author:

(i) decidability of the spectrum Sp(φ) of a local sentence φ, below ωω; where Sp(φ) is the set of ordinals α such that φ has a model of order type α

(ii) proof that bethω = sup{Sp(φ): φ local sentence with a bounded spectrum}

(iii) existence of a local sentence φ such that Sp(φ) contains all infinite ordinals except the inaccessible cardinals.
Automorphism–invariant measures on ℵ0-categorical structures without the independence property
Authors: Ensley Douglas E.
Published: May 2006

We address the classification of the possible finitely-additive probability measures on the Boolean algebra of definable subsets of M which are invariant under the natural action of Aut(M). This pursuit requires a generalization of Shelah's forking formulas [8] to “essentially measure zero” sets and an application of Myer's “rank diagram” [5] of the Boolean algebra under consideration. The classification is completed for a large class of ℵ0-categorical structures without the independence property including those which are stable.
A modified sentence unprovable in PA
Authors: Gordeev L.
Published: May 2006

H. Friedman proved that the following sentence SWQO() is true but not provable in the theory ATR0 (cf. [S]; ≔ the set of finite rooted trees, ∣T∣ ≔ the cardinality of T ∈ ).

For every k > 0 there is an n so large that for any T0, T1,…, Tn ∈ with ∀i ≤ n(∣Ti∣ ≤ k · (i + 1)) there are i < j ≤ n such that Ti is homeomorphically embeddable into Tj.

Since ATR0 is stronger than PA, SWQO() is not provable in PA, either. Furthermore, SWQO() is proof-theoretically stronger than PA. A similar sentence whose proof-theoretical strength is exactly that of PA was obtained by replacing finite trees by finite sequences of bounded natural numbers under the embeddability with H. Friedman's asymmetrical gap-condition (see [SS]). The latter sentence was modified by using the weaker symmetrical gap-condition (see the corresponding particular case in [Gl]). Further improvement is indicated in [G2, Corollary 4.5]. Namely, the assertion ∣Xi∣ ≤ k · (i + 1) as in SWQO(J), above, can be weakened to

.

(in fact, to wt(Xi) ≤ k + ε · i for an arbitrary fixed ε = l−1, l < 0, where wt(X) is the weight of the “word” X).
Small forcings and Cohen reals
Authors: Zapletal Jindřich
Published: May 2006

We show that all posets of uniform density ℵ1 may have to add a Cohen real and develop some forcing machinery for obtaining this sort of result.
On the relationship between ATR0 and
Authors: Avigad Jeremy
Published: May 2006

We show that the theory ATR0 is equivalent to a second-order generalization of the theory . As a result, ATR0 is conservative over for arithmetic sentences, though proofs in ATR0 can be much shorter than their counterparts.
Stable structures with few substructures
Authors: Laskowski Michael C. , Mayer Laura L.
Published: May 2006

A countable, atomically stable structure in a finite, relational language has fewer than 2ω non-isomorphic substructures if and only if is cellular. An example shows that the finiteness of the language is necessary.
Generalized quantification as substructural logic
Authors: Alechina Natasha , Lambalgen Michiel Van
Published: May 2006

We show how sequent calculi for some generalized quantifiers can be obtained by generalizing the Herbrand approach to ordinary first order proof theory. Typical of the Herbrand approach, as compared to plain sequent calculus, is increased control over relations of dependence between variables. In the case of generalized quantifiers, explicit attention to relations of dependence becomes indispensible for setting up proof systems. It is shown that this can be done by turning variables into structured objects, governed by various types of structural rules. These structured variables are interpreted semantically by means of a dependence relation. This relation is an analogue of the accessibility relation in modal logic. We then isolate a class of axioms for generalized quantifiers which correspond to first-order conditions on the dependence relation.
Cauchy completeness in elementary logic
Authors: Cifuentes J. C. , Sette A. M. , Mundici D.
Published: May 2006

The inverse of the distance between two structures≢of finite typeτis naturally measured by the smallest integerqsuch that a sentence of quantifier rankq− 1 is satisfied bybut not by. In this way the space Strτof structures of typeτis equipped with a pseudometric. The induced topology coincides with the elementary topology of Strτ. Using the rudiments of the theory of uniform spaces, in this elementary note we prove the convergence of every Cauchy net of structures, for any typeτ.
Forcing isomorphism II
Authors: Laskowski M. C. , Shelah S.
Published: May 2006

If T has only countably many complete types, yet has a type of infinite multiplicity then there is a c.c.c. forcing notion such that, in any -generic extension of the universe, there are non-isomorphic models M1 and M2 of T that can be forced isomorphic by a c.c.c. forcing. We give examples showing that the hypothesis on the number of complete types is necessary and what happens if ‘c.c.c’ is replaced by other cardinal-preserving adjectives. We also give an example showing that membership in a pseudo-elementary class can be altered by very simple cardinal-preserving forcings.
On countably closed complete Boolean algebras
Authors: Jech Thomas , Shelah Saharon
Published: May 2006

It is unprovable that every complete subalgebra of a countably closed complete Boolean algebra is countably closed.
Complete problems for fixed-point logics
Authors: Grohe Martin
Published: May 2006

The notion of logical reducibilities is derived from the idea of interpretations between theories. It was used by Lovász and Gács [LG77] and Immerman [Imm87] to give complete problems for certain complexity classes and hence establish new connections between logical definability and computational complexity.

However, the notion is also interesting in a purely logical context. For example, it is helpful to establish nonexpressibility results.

We say that a class of τ-structures is a >complete problem for a logic under L-reductions if it is definable in [τ] and if every class definable in can be ”translated” into by L-formulae (cf. §4).

We prove the following theorem:

1.1. Theorem. There are complete problemsfor partial fixed-point logic andfor inductive fixed-point logic under quantifier-free reductions.

The main step of the proof is to establish a new normal form for fixed-point formulae (which might be of some interest itself). To obtain this normal form we use theorems of Abiteboul and Vianu [AV91a] that show the equivalence between the fixed-point logics we consider and certain extensions of the database query language Datalog.

In [Dah87] Dahlhaus gave a complete problem for least fixed-point logic. Since least fixed-point logic equals inductive fixed-point logic by a well-known result of Gurevich and Shelah [GS86], this already proves one part of our theorem.

However, our class gives a natural description of the fixed-point process of an inductive fixed-point formula and hence sheds some light on completely different aspects of the logic than Dahlhaus's construction, which is strongly based on the features of least fixed-point formulae.
Possible behaviours of the reflection ordering of stationary sets
Authors: Witzany Jiří
Published: May 2006

If S, T are stationary subsets of a regular uncountable cardinal κ, we say that S reflects fully in T, S < T, if for almost all α ∈ T (except a nonstationary set) S ∩ α stationary in α. This relation is known to be a well-founded partial ordering. We say that a given poset P is realized by the reflection ordering if there is a maximal antichain 〈Xp: p ∈ P〉 of stationary subsets of Reg(κ) so that

We prove that if , and P is an arbitrary well-founded poset of cardinality ≤ κ+ then there is a generic extension where P is realized by the reflection ordering on κ.
The syntax and semantics of entailment in duality theory
Authors: Davey B. A. , Haviar M. , Priestley H. A.
Published: May 2006

Both syntactic and semantic solutions are given for the entailment problem of duality theory. The test algebra theorem provides both a syntactic solution to the entailment problem in terms of primitive positive formula and a new derivation of the corresponding result in clone theory, viz. the syntactic description of Inv(Pol(R)) for a given set R of unitary relations on a finite set. The semantic solution to the entailment problem follows from the syntactic one, or can be given in the form of an algorithm. It shows, in the special case of a purely relational type, that duality-theoretic entailment is describable in terms of five constructs, namely trivial relations, intersection, repetition removal, product, and retractive projection. All except the last are concrete, in the sense that they are described by a quantifier-free formula. It is proved that if the finite algebra M generates a congruence-distributive variety and all subalgebras of M are subdirectly irreducible, then concrete constructs suffice to describe entailment. The concept of entailment appropriate to strong dualities is also introduced, and described in terms of coordinate projections, restriction of domains, and composition of partial functions.
A reflection principle and its applications to nonstandard models
Authors: Schmerl James H.
Published: May 2006

Some methods of constructing nonstandard models work only for particular theories, such as ZFC, or CA + AC (which is second order number theory with the choice scheme). The examples of this which motivated the results of this paper occur in the main theorems of [5], which state that if T is any consistent extension of either ZFC0 (which is ZFC but with only countable replacement) or CA + AC and if κ and λ are suitably chosen cardinals, then T has a model which is κ-saturated and has the λ-Bolzano-Weierstrass property. (Compare with Theorem 3.5.) Another example is a result from [12] which states that if T is any consistent extension of CA + AC and cf (λ) > ℵ0, then T has a natural λ-Archimedean model. (Compare with Theorem 3.1 and the comments following it.) Still another example is a result in [6] in which it is shown that if a model of Peano arithmetic is expandable to a model of ZF or of CA, then so is any cofinal extension of . (Compare with Theorem 3.10.) Related types of constructions can also be found in [10] and [11].

A reflection principle will be proved here, allowing these constructions to be extended to models of many other theories, among which are some exceedingly weak theories and also all of their completions.
An induction principle and pigeonhole principles for K-finite sets
Authors: Blass Andreas
Published: May 2006

We establish a course-of-values induction principle for K-finite sets in intuitionistic type theory. Using this principle, we prove a pigeonhole principle conjectured by Bénabou and Loiseau. We also comment on some variants of this pigeonhole principle.
The largest countable inductive set is a mouse set
Authors: Rudominer Mitch
Published: May 2006

Let κℝ be the least ordinal κ such that Lκ (ℝ) is admissible. Let A = {x ϵ ℝ ∣ (∃α < κℝ) such that x is ordinal definable in Lα (ℝ)}. It is well known that (assuming determinacy) A is the largest countable inductive set of reals. Let T be the theory: ZFC − Replacement + “There exists ω Woodin cardinals which are cofinal in the ordinals.” T has consistency strength weaker than that of the theory ZFC + “There exists ω Woodin cardinals”, but stronger than that of the theory ZFC + “There exists n Woodin Cardinals”, for each n ϵ ω. Let M be the canonical, minimal inner model for the theory T. In this paper we show that A = ℝ ∩ M. Since M is a mouse, we say that A is a mouse set. As an application, we use our characterization of A to give an inner-model-theoretic proof of a theorem of Martin which states that for all n, every real is in A.
Interpolation and preservation for pebble logics
Authors: Baltag Alexandru
Published: May 2006

In Barwise and van Benthem [6], the authors give a general method for obtaining interpolation and preservation theorems for fragments of L∞ω, those for which there is a co-inductive pebble game Γ characterizing equivalence in the logic. The method is exemplified by an analysis of the following fragments: L∞ω itself, its existential fragment , its positive fragment , the k-variable fragment (and its existential and positive subfragments) and the modal fragment (and its existential and positive subfragments).

While most of their method is general, there is one part (showing that Γ has the Scott property relative to the fragment) that required a case-by-case analysis. The purpose of our paper is to replace this case-by-case analysis by a general theorem, and to illustrate this method by obtaining their kinds of results for some additional fragments of L∞ω.

Our general problem can be stated in the following way: Given a “nice” fragment F of L∞ω (one satisfying some natural closure conditions), find a pebble game characterization Γ of “preservation of F-formulas” and prove that Γ has the Scott property with respect to F. Applying the Abstract Interpolation Theorem from [6], we can conclude that F has Γ-interpolation, and the corresponding preservation result. In this paper, we shall give an answer to this question. (Our answer is “sufficient” but we don't know if our conditions are necessary.)
Coordinatisation and canonical bases in simple theories
Authors: Hart Bradd , Kim Byunghan , Pillay Anand
Published: May 2006

In this paper we discuss several generalization of theorems from stability theory to simple theories. Cherlin and Hrushovski, in [2] develop a substitute for canonical bases in finite rank, ω-categorical supersimple theories. Motivated by methods there, we prove the existence of canonical bases (in a suitable sense) for types in any simple theory. This is done in Section 2. In general these canonical bases will (as far as we know) exist only as “hyperimaginaries”, namely objects of the forma/Ewhereais a possibly infinite tuple andEa type-definable equivalence relation. (In the supersimple, ω-categorical case, these reduce to ordinary imaginaries.) So in Section 1 we develop the general theory of hyperimaginaries and show how first order model theory (including the theory of forking) generalises to hyperimaginaries. We go on, in Section 3 to show the existence and ubiquity of regular types in supersimple theories, ω-categorical simple structures and modularity is discussed in Section 4. It is also shown here how the general machinery of simplicity simplifies some of the general theory of smoothly approximable (or Lie-coordinatizable) structures from [2].

Throughout this paper we will work in a large, saturated modelMof a complete theoryT. All types, sets and sequences will have size smaller than the size ofM. We will assume that the reader is familiar with the basics of forking in simple theories as laid out in [4] and [6]. For basic stability-theoretic results concerning regular types, orthogonality etc., see [1] or [9].
Paires élémentaires de corps pseudo-finis: dénombrement des complétions (Elementary pairs of pseudo-finite fields: counting completions)
Authors: Lejeune Hélène
Published: May 2006

Let Π be a complete théorie of pseudo-finite fields. In this article we prove that, in the langage of fields to which we add a unary predicate for a substructure, the theory of non trivial elementary pairs of models of Π has completions, that is, the maximum that could exist.
A note on uniform definability and minimal fields of definition
Authors: Moosa Rahim
Published: May 2006

Let k ⊂ K be a field extension, where K is an algebraically closed field of any characteristic and k is the prime field. Recall the following property of Hilbert Schemes (see, for example, [1], Proposition 1.16): Suppose ⊂ × S is a flat family of closed subschemes of parametrised by a scheme S/k. Then for every closed subscheme Z ⊂ in , if [Z] denotes the Hilbert point of Z in Hilb() then the residue field of Hilb() at [Z] is the minimal field of definition for Z. Intuitively, this says that as a family parametrised by Hilb(), each fibre of lies above a point whose “co-ordinates” generate its minimal field of definition.

In the following note we are concerned with a more naive form of the above situation, for which we wish to give an elementary account. Suppose ϕ(x,y) is a system of polynomial equations over k (in variables x = (x1,…, xm) and parameters y = (y1, …, yn)), such that

is a family of (possibly reducible) affine varieties in Km. Each nonempty member of this family has a unique minimal field of definition. The question arises as to whether it is possible to express this family of varieties using parameters that come, pointwise, from these minimal fields of definition. That is, is there a system of polynomial equations ψ(x, z) over k, such that each ψ(x, b) with b ∈ KN is of the form Va for some a ∈ Kn; and such that each Va ∈ is defined by ψ(x, b) for some b ∈ KN whose coordinates generate the minimal field of definition for Va? Moreover, we would like b to be obtained definably from a.
Definability and undefinability with real order at the background
Authors: Gurevich Yuri , Rabinovich Alexander
Published: May 2006

We consider the monadic second-order theory of linear order. For the sake of brevity, linearly ordered sets will be called chains.

Let = ⟨A <⟩ be a chain. A formula ø(t) with one free individual variable t defines a point-set on A which contains the points of A that satisfy ø(t). As usually we identify a subset of A with its characteristic predicate and we will say that such a formula defines a predicate on A.

A formula (X) one free monadic predicate variable defines the set of predicates (or family of point-sets) on A that satisfy (X). This family is said to be definable by (X) in A. Suppose that is a subchain of = ⟨B, <⟩. With a formula (X, A) we associate the following family of point-sets (or set of predicates) {P : P ⊆ A and (P, A) holds in } on A. This family is said to be definable by in with at the background.

Note that in such a definition bound individual (respectively predicate) variables of range over B (respectively over subsets of B). Hence, it is reasonable to expect that the presence of a background chain allows one to define point sets (or families of point-sets) on A which are not definable inside .
There exist exactly two maximal strictly relevant extensions of the relevant logic R
Authors: Swirydowicz Kazimierz
Published: May 2006

In [60] N. Belnap presented an 8-element matrix for the relevant logic R with the following property: if in an implication A → B the formulas A and B do not have a common variable then there exists a valuation v such that v (A → B) does not belong to the set of designated elements of this matrix. A 6-element matrix of this kind can be found in: R. Routley, R.K. Meyer, V. Plumwood and R.T. Brady [82], Below we prove that the logics generated by these two matrices are the only maximal extensions of the relevant logic R which have the relevance property: if A → B is provable in such a logic then A and B have a common propositional variable.
Weakly o-minimal structures and some of their properties
Authors: Kulpeshov B. SH.
Published: May 2006

The main result of this paper is Theorem 3.1 which is a criterion for weak o-minimality of a linearly ordered structure in terms of realizations of 1-types. Here we also prove some other properties of weakly o-minimal structures. In particular, we characterize all weakly o-minimal linear orderings in the signature {<, =} . Moreover, we present a criterion for density of isolated types of a weakly o-minimal theory. Lastly, at the end of the paper we present some remarks on the Exchange Principle for algebraic closure in a weakly o-minimal structure.
Was Sierpiński right? IV
Authors: Shelah Saharon
Published: May 2006

We prove for any μ = μ<μ < θ < λ. λ large enough (just strongly inaccessible Mahlo) the consistency of and even for σ < μ. The new point is that possibly 0 > μ+.
Computability over the partial continuous functionals
Authors: Normann Dag
Published: May 2006

We show that to every recursive total continuous functional Φ there is a PCF-definable representative Ψ of Φ in the hierarchy of partial continuous functionals, where PCF is Plotkin's programming language for computable functionals. PCF-definable is equivalent to Kleene's S1–S9-computable over the partial continuous functionals.
Completions of PA: Models and enumerations of representable sets
Authors: McAllister Alex M.
Published: May 2006

We generalize a result on True Arithmetic (ℐA) by Lachlan and Soare to certain other completions of Peano Arithmetic (PA). If ℐ is a completion of PA, then Rep(ℐ) denotes the family of sets X ⊆ ω for which there exists a formula φ(x) such that for all n ∈ ω, if n ∈ X, then ℐ ⊢ φ(S(n) (0)) and if n ∉ X, then ℐ ⊢ ┐φ(S(n)(O)). We show that if S, J ⊆ P(ω) such that S is a Scott set, J is a jump ideal, S ⊂ J and for all X ∈ J, there exists C ∈ S such that C is a “coding” set for the family of subtrees of 2<ω computable in X, and if ℐ is a completion of PA Such that Rep(ℐ) = S, then there exists a model A of ℐ such that J is the Scott set of A and no enumeration of Rep(ℐ) is computable in A. The model A of ℐ is obtained via a new notion of forcing.

Before proving our main result, we demonstrate the existence of uncountably many different pairs (S, J) satisfying the conditions of our theorem. This involves a new characterization of 1-generic sets as coding sets for the computable subtrees of 2<ω. In particular, C C ⊆ ω is a coding set for the family of subtrees of 2<ω computable in X if and only if for all trees T ⊆ 2<ω computable in X, if χc is a path through T, then there exists σ ∈ T such that σ ⊂ χc and every extension of σ is in T. Jockusch noted a connection between 1-generic sets and coding sets for computable subtrees of 2<ω. We show they are identical.
Decidability of cylindric set algebras of dimension two and first-order logic with two variables
Authors: Marx Maarten , Mikulás Szabolcs
Published: May 2006

The aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse2). The new proof also shows the known results that the universal theory of Pse2 is decidable and that every finite Pse2 can be represented on a finite base. Since the class Cs2 of cylindric set algebras of dimension 2 forms a reduct of Pse2, these results extend to Cs2 as well.
On measurable limits of compact cardinals
Authors: Apter Arthur W.
Published: May 2006

We extend earlier work (both individual and joint with Shelah) and prove three theorems about the class of measurable limits of compact cardinals, where a compact cardinal is one which is either strongly compact or supercompact. In particular, we construct two models in which every measurable limit of compact cardinals below the least supercompact limit of supercompact cardinals possesses non-trivial degrees of supercompactness. In one of these models, every measurable limit of compact cardinals is a limit of supercompact cardinals and also a limit of strongly compact cardinals having no non-trivial degree of supercompactness. We also show that it is consistent for the least supercompact cardinal κ to be a limit of strongly compact cardinals and be so that every measurable limit of compact cardinals below κ has a non-trivial degree of supercompactness. In this model, the only compact cardinals below κ with a non-trivial degree of supercompactness are the measurable limits of compact cardinals.
Some results on combinators in the system TRC
Authors: Jech Thomas
Published: May 2006

We investigate the system TRC of untyped illative combinatory logic that is equiconsistent with New Foundations. We prove that various unstratified combinators do not exist in TRC.
Regular subalgebras of complete Boolean algebras
Authors: Błaszczyk Aleksander , Shelah Saharon
Published: May 2006

It is proved that the following conditions are equivalent:

(a) there exists a complete, atomless, σ–centered Boolean algebra, which does not contain any regular, atomless, countable subalgebra.

(b) there exists a nowhere dense ultrafilter on ω.

Therefore, the existence of such algebras is undecidable in ZFC. In “forcing language” condition (a) says that there exists a non–trivial σ–centered forcing not adding Cohen reals.
A polarized partition relation using elementary substructures
Authors: Jones Albin L.
Published: May 2006

Working in ZFC, we show that for any infinite cardinal k and ordinal y < (2<k)+ the polarized partition relation

holds. Our proof of this relation involves the use of elementary substructures of set models of large fragments of ZFC.
On the commutativity of jumps
Authors: McNicholl Timothy H.
Published: May 2006

We study the following classes:

● Q* (r1A1…..rkAk) which is defined to be the collection of all sets that can be computed by a Turing machine that on any input makes a total of ri, queries to Ai, for all i ∈ {1..… k}.

● Q(r1A1…..rkAk) which is defined like Q* (r1A1….. rkAk) except that queries to Ai, must be made before queries to Ai+1 for all i ∈ {1….. k – 1}.

● QC(r1A1….. rkAk) which is defined like Q{r1A1….. rkAk) except that the Turing machine must halt even if given incorrect answers to some of its queries.

We show that if A1 ….. Ak are jumps that are not too close together, then all three of these classes are identical and are not changed if we permute (r1…..rkAk). This extends a result of Beigel's [1]. Since the second class is not affected by permutations, we say that these sets commute with each other. We also show that jumps that are too close together may not commute. We also characterize the commutative sequences of sets obtained by iterating the jump operation through an ordinal notation.
Canonicity for Intensional Logics with Even Axioms
Authors: Surendonk Timothy J.
Published: May 2006

This paper looks at the concept of neighborhood canonicity introduced by Brian Chellas [2]. We follow the lead of the author's paper [9] where it was shown that every non-iterative logic is neighborhood canonical and here we will show that all logics whose axioms have a simple syntactic form—no intensional operator is in boolean combination with a propositional letter—and which have the finite model property are neighborhood canonical. One consequence of this is that KMcK, the McKinsey logic, is neighborhood canonical, an interesting counterpoint to the results of Robert Goldblatt and Xiaoping Wang who showed, respectively, that KMcK is not relational canonical [5] and that KMcK is not relationally strongly complete [11].
Quantifier elimination in tame infinite p-adic fields
Authors: Brigandt Ingo
Published: May 2006

We give an answer to the question as to whether quantifier elimination is possible in some infinite algebraic extensions of ℚp (‘infinite p-adic fields’) using a natural language extension. The present paper deals with those infinite p-adic fields which admit only tamely ramified algebraic extensions (so-called tame fields). In the case of tame fields whose residue fields satisfy Kaplansky's condition of having no extension of p-divisible degree quantifier elimination is possible when the language of valued fields is extended by the power predicates Pn introduced by Macintyre and, for the residue field, further predicates and constants. For tame infinite p-adic fields with algebraically closed residue fields an extension by Pn predicates is sufficient.
Anxiety, Enthusiasm, and the Vote: The Emotional Underpinnings of Learning and Involvement During Presidential Campaigns
Authors: Marcus George E. , MacKuen Michael B.
Published: May 2006

By incorporating emotionality, we propose to enrich information-processing models of citizens' behavior during election campaigns. We demonstrate that two distinct dynamic emotional responses play influential roles during election campaigns: anxiety and enthusiasm. Anxiety, responding to threat and novelty, stimulates attention toward the campaign and political learning and discourages reliance on habitual cues for voting. Enthusiasm powerfully influences candidate preferences and stimulates interest and involvement in the campaign. The findings support a theoretical perspective that regards cognitive and emotional processes as mutually engaged and mutually supportive rather than as antagonistic. We suggest that the democratic process may not be undermined by emotionality as is generally presupposed. Instead, we believe that people use emotions as tools for efficient information processing and thus enhance their abilities to engage in meaningful political deliberation.
The Supreme Court as a Countermajoritarian Institution? The Impact of Public Opinion on Supreme Court Decisions
Authors: Mishler William , Sheehan Reginald S.
Published: May 2006

Although normative questions about the role of the Supreme Court as a countermajoritarian institution have long excited controversy in democratic theory, empirical questions about how far the Court acts contrary to majoritarian opinion have received less attention. Time series analyses for the period 1956–89 indicate the existence of a reciprocal and positive relationship between long-term trends in aggregate public opinion and the Court's collective decisions. The Court's ideological composition changes in response to previous shifts in the partisan and ideological orientation of the president and Congress. The Court also responds to public opinion at the margins even in the absence of membership change. Since 1981, the relationship has vanished or turned negative in direction. The Court's ideological balance has been upset by an unbroken string of conservative-to-moderate appointments, thereby undermining the dynamics that promote judicial responsiveness and raising questions about the majoritarianism of the contemporary and future Court.
Comparing Centralized and Decentralized Institutions: A Reply to Schwartz and Tomz
Authors: Bendor Jonathan , Mookherjee Dilip
Published: May 2006

Schwartz and Tomz (1997) have correctly pointed out an error in our 1987 article: We had neglected to analyze how changes in group composition improve the performance of centralized institutions over time. The change affects only the case of perfect monitoring, however. We argue, moreover, that even in this special context, our main qualitative conclusion—that the centralized structure has no positive advantage over the decentralized one—continues to hold. We reach different conclusions about the relative roles of the two institutions, partly because we had in mind a positive interpretation, whereas Schwartz and Tomz select a normative interpretation of the issue of institutional choice. Finally, we believe that imperfect monitoring is essential to the theory, in order to derive conclusions that are not driven by artifacts of the model or by arbitrary equilibrium selections.
Beyond Quid Pro Quo: What's Wrong with Private Gain from Public Office?
Authors: Stark Andrew
Published: May 2006

The longstanding debate over whether officials should be permitted to profit personally from public office has moved to the center of public discourse in the United States. As the HouseEthics Manualput it recently, it is of concern simply when an officeholder “cash[es] in on official position,” regardless of whether his or her official performance was in any way impaired as a result. Although the question of private gain from public office is richly implicative of a number of fundamental issues in political theory—in particular the ongoing controversy over where to draw the borders between private and public as well as the nature of official fiduciary responsibility—it has yet to undergo political-theoretic analysis. In what follows, I examine both the conceptual and normative issues emergent in the debate over private gain from public office.
Trends in the Partisan Composition of State Legislatures: A Response to Fiorina
Authors: Stonecash Jeffrey M. , Agathangelou Anna M.
Published: May 2006

The percentage of state legislative seats won by Democrats in nonsouthern states has increased steadily since World War II. Fiorina (1994) argues that this is because of the professionalization of state legislatures: Legislatures now meet longer and pay higher salaries; legislative positions which require more time are less attractive to Republicans, who can make more money elsewhere; higher salaries attract Democrats, who make less in the private sector. That analysis has several serious flaws. First, nonsouthern states have gradually become more Democratic at all levels as part of a long-term regional political realignment. The rise in Democrats in legislatures outside the South is due more to this realignment than to legislative professionalization. Second, trends in southern states contradict his hypothesis. Professionalization has increased, but state legislatures are becoming more Republican. Finally, Fiorina's analysis is worth careful reconsideration because it suggests that there is little connection between constituencies and partisan outcomes.
On Post's canonical systems
Authors: Smullyan Raymond M.
Published: May 2006

We assume familiarity with the canonical languages of Post (cf. [1], [2]).

A set S of strings is said to be representable in a canonical system (F) if there is a string π such that for every string X, X ∈ S if and only if πX is provable in (F).

Suppose that K is a finite alphabet containing at least 2 symbols, and that W is a set of strings in (the symbols of) K. If W is representable in some canonical system, is it necessarily representable in a canonical system which uses only the symbols of K ? We answer this question affirmatively. Thus, e.g., it is possible to construct a 2-sign universal system over its own alphabet.2
On weak completeness of intuitionistic predicate logic
Authors: Kreisel G.
Published: May 2006

Suppose the ri-placed relation symbols Pi, 1 ≦ i ≦ k, are all the non-logical constants occurring in the closed formula , also written as , of Heyting's predicate calculus (HPC). Then HPC is called complete for provided , i.e.

Here D ranges over arbitrary species, and over arbitrary (possibly incompletely defined) subspecies of ;
The sentential calculus using rule of inference Re
Authors: Angell R. B.
Published: May 2006

Axiomatizations of the sentential calculus which use Rmp (modus ponens), have been shown equivalent to axiomatizations similar in all respects except that Rmp is replaced by the less restricted rule Re (rule of excision)1:

Re. If S and (…(S⊃S') …), then (… S' …).
Organization of frontoparietal cortex in the tree shrew (Tupaia belangeri). I. Architecture, microelectrode maps, and corticospinal connections
Authors: Remple Michael S. , Reed Jamie L. , Stepniewska Iwona , Kaas Jon H.
Published: May 2006

Despite extensive investigation of the motor cortex of primates, little is known about the organization of motor cortex in tree shrews, one of their closest living relatives. We investigated the organization of frontoparietal cortex in Belanger's tree shrews (Tupaia belangeri) by using intracortical microstimulation (ICMS), corticospinal tracing, and detailed histological analysis. The results provide evidence for the subdivision of tree shrew frontoparietal cortex into seven distinct areas (five are newly identified), including two motor fields (M1 and M2) and five somatosensory fields (3a, 3b, S2, PV, and SC). The types of movements evoked in M1 and M2 were similar, but M2 required higher currents to elicit movements and had few connections to the cervical spinal cord and distinctive cyto‐ and immunoarchitecture. The borders between M1 and the anterior somatosensory regions (3a and 3b) were identified primarily from histological analysis, because thresholds were similar between these regions, and differences in corticospinal neuron distribution were subtle. The caudal (SC) and lateral (S2 and PV) somatosensory fields were identified based on differences in architecture and distribution of corticospinal neurons. Myelin‐dense modules were identified in lateral cortex, in the expected location of the oral, forelimb, and hindlimb representations of S2, and possibly PV. Evidence for a complex primate‐like array of motor fields is lacking in tree shrews, but their motor cortex shares a number of basic features with that of primates, which are not found in more distantly related species, such as rats. J. Comp. Neurol. 497:133–154, 2006. © 2006 Wiley‐Liss, Inc.
Does temperamental instability support a continuity between bipolar II disorder and major depressive disorder?
Authors: Benazzi F.
Published: May 2006

Background

The current categorical split of mood disorders in bipolar disorders and depressive disorders has recently been questioned. Two highly unstable personality features, i.e. the cyclothymic temperament (CT) and borderline personality disorder (BPD), have been found to be more common in bipolar II (BP-II) disorder than in major depressive disorder (MDD). According to Kraepelin, temperamental instability was the ‘foundation’ of his unitary view of mood disorders.

Study aim

The aim was to assess the distributions of the number of CT and borderline personality items between BP-II and MDD. Finding no bi-modal distribution (a ‘zone of rarity’) of these items would support a continuity between the two disorders.

Methods

Study setting: an outpatient psychiatry private practice. Interviewer: A senior clinical and mood disorder research psychiatrist. Patient population: A consecutive sample of 138 BP-II and 71 MDD remitted outpatients. Assessment instruments: The structured clinical interview for DSM-IV Axis I Disorders-Clinician Version (SCID-CV), the SCID-II Personality Questionnaire for self-assessing borderline personality traits (BPT) by patients, the TEMPS-A for self-assessing CT by patients. Interview methods: Patients were interviewed with the SCID-CV to diagnose BP-II and MDD, and then patients self-assessed the questions of the Personality Questionnaire relative to borderline personality, and the questions of the TEMPS-A relative to CT. As clinically significant distress or impairment of functioning is not assessed by the SCID-II Personality Questionnaire, a diagnosis of BPD could not be made, but BPT could be assessed (i.e. all BPD items but not the impairment criterion). The distribution of the number of CT and BPT items was studied by Kernel density estimate.

Results

CT and BPT items were significantly more common in BP-II versus MDD. The Kernel density estimate distributions of the number of CT and BPT items in the entire sample had a normal-like shape (i.e. no bi-modality).

Conclusions

The expected finding, on the basis of previous studies and of the present sample features, was a clustering of CT and BPT items on the BP-II side of the curves. Instead, no bi-modality was present in the distributions of the number of CT and BPT items in the entire sample, showing a normal-like shape. By using the bi-modality approach, a continuity between BP-II and MDD seems supported, questioning the current categorical splitting of BP-II and MDD based on classic diagnostic validators.
Nobiletin, a citrus flavonoid, suppresses phorbol ester‐induced expression of multiple scavenger receptor genes in THP‐1 human monocytic cells
Authors: Eguchi Ai , Murakami Akira , Ohigashi Hajime
Published: May 2006

Unregulated uptake of oxidized low‐density lipoproteins (ox‐LDL) via macrophage scavenger receptors (SRs) such as lectin‐like ox‐LDL receptor‐1 (LOX‐1) is a key event in atherosclerosis. In this study, we examined the effects of five selected food phytochemicals on 12‐O‐tetradecanoylphorbol‐13‐acetate (TPA)‐induced LOX‐1 mRNA expression in THP‐1 human monocyte‐like cells. Nobiletin, a citrus polymethoxylated flavone, markedly reduced it in dose‐ and time‐dependent manners. It also suppressed the phosphorylation of extracellular signal‐regulated protein kinase (ERK) 1/2, c‐Jun NH2‐terminal kinase (JNK) 1/2, and c‐Jun (Ser‐63), thereby inhibiting the transcriptional activity of activator protein‐1. Further nobiletin attenuated expression of SR‐A, SR‐PSOX, CD36, and CD68, but not CLA‐1, mRNA, leading to the blockade of DiI‐acLDL uptake. Together, our results suggest that nobiletin is a promising phytochemical for regulating atherosclerosis with reasonable action mechanisms.
Equilibrium configurations of an infinite cylinder in an unbounded fluid
Authors: Bhatnagar Rajat , Finn Robert
Published: May 2006

In the context of the adjoining paper by Finn [Phys. Fluids 18, 047102 (2006)] that questions the validity of the Young diagram, we consider equilibrium configurations of an infinite solid circular cylinder floating horizontally in an unlimited bath, in the presence of a vertically downward gravity field. We characterize equilibria both from a force balance point of view and also as stationary points for an energy functional. In the former sense, the question arises as to the sense in which “solid/liquid” surface tensions introduced by Young should be envisaged in the force balance; we find in accordance with Finn’s observation that their introduction would yield an erroneous result. We confirm our view further by an explicit energy analysis, which additionally yields stability information for the stationary points. Depending on the data, multiple solutions can appear; we show that whenever that occurs, only one of the solutions is locally stable. A peculiar property of these points is that each of them is “emphatically stationary” in the sense that the energy variation vanishes not only in directions within the geometric constraint, but also in directions orthogonal to it.
Nonlinear dynamos in laminar, helical pipe flow
Authors: Zabielski L. , Mestel A. J.
Published: May 2006

Steady, pressure-driven incompressible laminar flow of an electrically conducting fluid down a helically symmetric pipe is known to be capable of sustaining a dynamo at a fairly low hydrodynamic Reynolds number. The nonlinear time evolution of such a dynamo is investigated. Both the fluid motion and the magnetic field are assumed to be helically symmetric. As the magnetic Reynolds number is increased, the dynamo first saturates with a steady field. Subsequently, time-periodic solutions occur exhibiting field reversal. Eventually a-periodic behavior is found, with quasiperiodic bursts and field reversals. Occasionally the field is all but totally quenched, reestablishing itself on the long time scale of the linear eigenfunction.