bluuebunny/crossref_metadata_2025 huggingface dataset:
Some elementary results in intuitionistic model theory
Authors: Veldman Wim , Waaldijk Frank
Published: May 2006

We establish constructive refinements of several well-known theorems in elementary model theory. The additive group of the real numbers may be embedded elementarily into the additive group of pairs of real numbers, constructively as well as classically.
The Morley rank of a Banach space
Authors: Iovino José
Published: May 2006

We introduce the concepts of Morley rank and Morley degree for structures based on Banach spaces. We characterize ω-stability in terms of Morley rank, and prove the existence of prime models for ω-stable theories.
The existence of finitely based lower covers for finitely based equational theories
Authors: Ježek Jaroslav , McNulty George F.
Published: May 2006

By an equational theory we mean a set of equations from some fixed language which is closed with respect to logical consequences. We regard equations as universal sentences whose quantifier-free parts are equations between terms. In our notation, we suppress the universal quantifiers. Once a language has been fixed, the collection of all equational theories for that language is a lattice ordered by set inclusion The meet in this lattice is simply intersection; the join of a collection of equational theories is the equational theory axiomatized by the union of the collection. In this paper we prove, for languages with only finitely many fundamental operation symbols, that any nontrivial finitely axiomatizable equational theory covers some other finitely axiomatizable equational theory. In fact, our result is a little more general.

There is an extensive literature concerning lattices of equational theories. These lattices are always algebraic. Compact elements of these lattices are the finitely axiomatizable equational theories. We also call themfinitely based. The largest element in the lattice is compact; it is the equational theory based on the single equationx≈y. The smallest element of the lattice is thetrivial theoryconsisting of tautological equations. For all but the simplest languages, the lattice of equational theories is intricate. R. McKenzie in [6] was able to prove in essence that the underlying language can be recovered from the isomorphism type of this lattice.
as an initial segment of the c-degrees
Authors: Groszek Marcia
Published: May 2006

By an “inverse iteration” of Sacks forcing over a model of V = L, we produce a model in which the degrees of constructibility of nonconstructible reals have order type
Lascar strong types in some simple theories
Authors: Buechler Steven
Published: May 2006

In this paper a class of simple theories, called the low theories is developed, and the following is proved.

Theorem. Let T be a low theory, A a set and a, b elements realizing the same strong type over A. Then, a and b realize the same Lasear strong type over A.
A non-standard construction of Haar measure and weak König's lemma
Authors: Tanaka Kazuyuki , Yamazaki Takeshi
Published: May 2006

In this paper, we show within RCA0 that weak König's lemma is necessary and sufficient to prove that any (separable) compact group has a Haar measure. Within WKL0, a Haar measure is constructed by a non-standard method based on a fact that every countable non-standard model of WKL0 has a proper initial part isomorphic to itself [10].
Property theory and the revision theory of definitions
Authors: Orilia Francesco
Published: May 2006

§1. Introduction.Russell's type-theory can be seen as a theory of properties, relations, and propositions (PRPs) (in short, a property theory). It relies on rigid type distinctions at the grammatical level to circumvent the property theorist's major problem, namely Russell's paradox, or, more generally, the paradoxes of predication. Type theory has arguably been the standard property theory for years, often taken for granted, and used in many applications. In particular, Montague [27] has shown how to use a type-theoretical property-theory as a foundation for natural language semantics.

In recent years, it has been persuasively argued that many linguistic and ontological data are best accounted for by using a type-free property theory. Several type-free property theories, typically with fine-grained identity conditions for PRPs, have therefore been proposed as potential candidates to play a foundational role in natural language semantics, or for related applications in formal ontology and the foundations of mathematics (Bealer [6], Cocchiarella [18], Turner [35], etc.).

Attempts have then been made to combine some such property theory with a Montague-style approach in natural language semantics. Most notably, Chierchia and Turner [15] propose a Montague-style semantic analysis of a fragment of English, by basically relying on the type-free system of Turner [35]. For a similar purpose Chierchia [14] relies on one of the systems based on homogeneous stratification due to Cocchiarella. Cocchiarella's systems have also been used for applications in formal ontology, inspired by Montague's account of quantifier phrases as, roughly, properties of properties (see, e.g., Cocchiarella [17], [19], Landini [25], Orilia [29]).
Weakly algebraizable logics
Authors: Czelakowski Janusz , Jansana Ramon
Published: May 2006

In the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.
The real line in elementary submodels of set theory
Authors: Kunen Kenneth , Tall Franklin D.
Published: May 2006

The use of elementary submodels has become a standard tool in set-theoretic topology and infinitary combinatorics. Thus, in studying some combinatorial objects, one embeds them in a set, M, which is an elementary submodel of the universe, V (that is, (M; Є) ≺ (V; Є)). Applying the downward Löwenheim-Skolem Theorem, one can bound the cardinality of M. This tool enables one to capture various complicated closure arguments within the simple “≺”.

However, in this paper, as in the paper [JT], we study the tool for its own sake. [JT] discussed various general properties of topological spaces in elementary submodels. In this paper, we specialize this consideration to the space of real numbers, ℝ. Our models M are not in general transitive. We will always have ℝ Є M, but not usually ℝ ⊆ M. We plan to study properties of the ℝ ⋂ M's. In particular, as M varies, we wish to study whether any two of these ℝ ⋂ M's are isomorphic as topological spaces, linear orders, or fields.

As usual, it takes some sleight-of-hand to formalize these notions within the standard axioms of set theory (ZFC), since within ZFC, one cannot actually define the notion (M;Є) ≺ (V;Є). Instead, one proves theorems about M such that (M;Є) ≺ (H(θ);Є), where θ is a “large enough” cardinal; here, H(θ) is the collection of all sets whose transitive closure has size less than θ.
Un principe d'ax-kochen-ershov pour des structures intermédiates entre groupes et corps valués
Authors: Delon Françoise , Simonetta Patrick
Published: May 2006

An Ax-Kochen-Ershov principle for intermediate structures between valued groups and valued fields.

We will consider structures that we call valued B-groups and which are of the form 〈G, B, *, υ〉 where

– G is an abelian group,

– B is an ordered group,

– υ is a valuation denned on G taking its values in B,

– * is an action of B on G satisfying: ∀x ϵ G ∀ b ∈ B υ(x * b) = ν(x) · b.

The analysis of Kaplanski for valued fields can be adapted to our context and allows us to formulate an Ax-Kochen-Ershov principle for valued B-groups: we axiomatise those which are in some sense existentially closed and also obtain many of their model-theoretical properties. Let us mention some applications:

1. Assume that υ(x) = υ(nx) for every integer n ≠ 0 and x ϵ G, B is solvable and acts on G in such a way that, for the induced action, Z[B] ∖ {0} embeds in the automorphism group of G. Then 〈G, B, *, υ〉 is decidable if and only if B is decidable as an ordered group.

2. Given a field k and an ordered group B, we consider the generalised power series field k((B)) endowed with its canonical valuation. We consider also the following structure:

where k((B))+ is the additive group of k((B)), S is a unary predicate interpreting {Tb ∣ b ϵB}, and ×↾k((B))×S is the multiplication restricted to k((B)) × S, structure which is a reduct of the valued field k((B)) with its canonical cross section. Then our result implies that if B is solvable and decidable as an ordered group, then M is decidable.

3. A valued B–group has a residual group and our Ax-Kochen-Ershov principle remains valid in the context of expansions of residual group and value group. In particular, by adding a residual order we obtain new examples of solvable ordered groups having a decidable theory.
Grafted frames and S1 -completeness
Authors: Zhou Beihai
Published: May 2006

A grafted frame is a new kind of frame which combines a modal frame and some relevance frames. A grafted model consists of a grafted frame and a truth-value assignment. In this paper, the grafted frame and the grafted model are constructed and used to show the completeness of S1. The implications of S1-completeness are discussed.

A grafted frame does not combine two kinds of frames simply by putting relations defined in the components together. That is, the resulting grafted frame is not in the form of , or more generally, in the form of ,…>, which consists of a non-empty set with several relations defined on it.1 Rather, it resembles the construction of fibering proposed by D. M. Gabbay and M. Finger (see [4] and [3]). On a grafted frame, some modal worlds, which belong to the initial modal frame, are attached by some relevance frames.

However, these two semantics have important differences. Consider the combined semantics involving semantics of relevance logic and modal logic. A fibred model and a grafted model proposed in this paper differ in the following respects. First, a fibred model is constructed from a class of modal models and a class of relevance models. A grafted model consists of a grafted frame and a truth-value assignment, where the grafted frame is constructed from a modal frame and some relevance frames, and the assignment is a union of a modal truth-value assignment VM and some relevance truth-value assignments VR. VM (VR) defined in this paper is not the same as the assignment contained in a modal (relevance) model. Second, in a fibred model each relevance world is associated (or fibred) with a modal model and each modal world with a relevance model.2 To be the grafted frame on which a grafted model is based, it is enough to have some modal worlds attached by some relevance frames. Moreover, no relevance world is associated with a modal frame in the grafted frame. Third, fibred models are intended to provide an appropriate semantics to combined logics. Grafted frames and grafted models are inspired to characterize S1, which, containing only one modality □, is not a combined logic. It is shown in this paper that S1 is sort of a meta-logic of the intersection of S0.4 and F, where S0.4, a new system proposed in this paper, is in turn a meta-logic of the relevance logic.
The cylindric algebras of three-valued logic
Authors: Feldman Norman
Published: May 2006

In this paper we consider the three-valued logic used by Kleene [6] in the theory of partial recursive functions. This logic has three truth values: true (T), false (F), and undefined (U). One interpretation of U is as follows: Suppose we have two partially recursive predicates P(x) and Q(x) and we want to know the truth value of P(x) ∧ Q(x) for a particular x0. If x0 is in the domain of definition of both P and Q, then P(x0) ∧ Q(x0) is true if both P(x0) and Q(x0) are true, and false otherwise. But what if x0 is not in the domain of definition of P, but is in the domain of definition of Q? There are several choices, but the one chosen by Kleene is that if Q(X0) is false, then P(x0) ∧ Q(x0) is also false and if Q(X0) is true, then P(x0) ∧ Q(X0) is undefined.

What arises is the question about knowledge of whether or not x0 is in the domain of definition of P. Is there an effective procedure to determine this? If not, then we can interpret U as being unknown. If there is an effective procedure, then our decision for the truth value for P(x) ∧ Q(x) is based on the knowledge that is not in the domain of definition of P. In this case, U can be interpreted as undefined. In either case, we base our truth value of P(x) ∧ Q(x) on the truth value of Q(X0).
Termination and confluence in infinitary term rewriting
Authors: Rodenburg P. H.
Published: May 2006

The basic notions of the theory of term rewriting are defined for terms that may involve function letters of infinite arity. A sufficient condition for completeness is derived, and its use demonstrated by the example of abstract clones over infinitary signatures.
Compactness of Lobe spaces
Authors: Jin Renling , Shelah Saharon
Published: May 2006

In this paper we show that the compactness of a Loeb space depends on its cardinality, the nonstandard universe it belongs to and the underlying model of set theory we live in. In §1 we prove that Loeb spaces are compact under various assumptions, and in §2 we prove that Loeb spaces are not compact under various other assumptions. The results in §1 and §2 give a quite complete answer to a question of D.Ross in [9], [11] and [12].
An ordinal partition avoiding pentagrams
Authors: Larson Jean A.
Published: May 2006

Suppose that α = γ + δ where γ ≥ δ > 0. Then there is a graph which has no independent set of order type and has no pentagram (a pentagram is a set of five points with all pairs joined by edges). In the notation of Erdős and Rado. who generalized Ramsey's Theorem to this setting.
Eventually infinite time Turing machine degrees: infinite time decidable reals
Authors: Welch P.D.
Published: May 2006

We characterise explicitly the decidable predicates on integers of Infinite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down ζ, the least ordinal not the length of any eventual output of an Infinite Time Turing machine (halting or otherwise); using this the Infinite Time Turing Degrees are considered, and it is shown how the jump operator coincides with the production of mastercodes for the constructible hierarchy; further that the natural ordinals associated with the jump operator satisfy a Spector criterion, and correspond to the Lζ-stables. It also implies that the machines devised are “Σ2 Complete” amongst all such other possible machines. It is shown that least upper bounds of an “eventual jump” hierarchy exist on an initial segment.
Model companions of theories with an automorphism
Authors: Kikyo Hirotaka
Published: May 2006

For a theory T in L, Tσ is the theory of the models of T with an automorphism σ. If T is an unstable model complete theory without the independence property, then Tσ has no model companion. If T is an unstable model complete theory and Tσ has the amalgamation property, then Tσ has no model companion. If T is model complete and has the fcp, then Tσ has no model completion.
Nowhere precipitousness of some ideals
Authors: Matsubara Yo , Shioya Masahiro
Published: May 2006

In this paper we will present a simple condition for an ideal to be nowhere precipitous. Through this condition we show nowhere precipitousness of fundamental ideals onPkλ, in particular the non-stationary idealNSkλunder cardinal arithmetic assumptions.

In this sectionIdenotes a non-principal ideal on an infinite setA. LetI+=PA/I(ordered by inclusion as a forcing notion) andI∣X= {Y⊂A:Y⋂X∈I}, which is also an ideal onAforX∈I+. We refer the reader to [8, Section 35] for the general theory of generic ultrapowers associated with an ideal. We recallIis said to be precipitous if ⊨I+“Ult(V, Ġ) is well-founded” [9].

The central notion of this paper is a strong negation of precipitousness [1]:

Definition.Iis nowhere precipitous ifI∣Xis not precipitous for everyX∈ I+i.e., ⊨I+“Ult(V, Ġ) is ill-founded.”

It is useful to characterize nowhere precipitousness in terms of infinite games (see [11, Section 27]). Consider the following gameG(I) between two players, Nonempty and Empty [5]. Nonempty and Empty alternately chooseXn∈I+andYn∈I+respectively so thatXn⊃Yn⊃n+1. After ω moves, Empty wins the game if⋂n<ωXn=⋂n<ωYn= Ø.

See [5, Theorem 2] for a proof of the following characterization.

Proposition.I is nowhere precipitous if and only if Empty has a winning strategy in G(I).
Ordre fondamental d'une théorie 1-basée
Authors: Bagheri Seyyed Mohammad
Published: May 2006

D'après Lascar et Poizat [10], la déviation pour une théorie stable est associée à un préordre partiel sur l'ensemble des types. L'ordre induit a été nommé par Poizat ordre fondamental. Il mesure combien un type est loin d'être réalisé et il donne un certain nombre d'informations sur la théorie. Une question naturelle, est de décrire completément tous les ordres fondamentaux [13]. Il semble que cela soit difficile. Un problème moins ambitieux est de trouver des conditions pour qu'un ordre soit l'ordre fondamental d'une théorie, ou bien de trouver des exemples.

Le but de cet article est de trouver de nouveaux exemples d'ordres fondamentaux. Nous nous concentrons principalement sur les théories stables et 1-basées car, comme nous allons voir dans la Section 2, avec cette hypothèse, il y a une représentation simple de l'ordre fondamental grâce aux ensembles algébriquement clos d'éléments des modèles de la thé;orie considégrée. Dans la Section 3, nous généralisons une idée de Baldwin et Berman [2] pour construire de “nouveaux” exemples d'ordres fondamentaux. En combinant cette construction avec les résultats de la Section 2, on caractérise de manière complete les ordres fondamentaux de theories triviales et 1-basées: les blocs des ordres fondamentaux d'une théorie triviale et 1-basée sont les inverses des posets de la forme I(L)/G où L est un treillis distributif borné et G un groupe compact d'automorphismes localement fini de L. De plus, tout ordre partiel de cette forme est l'ordre fondamental d'une théorie triviale et 1-basá. En particulier, l'ordre fondamental n'est pas toujours un treillis.
Cantor-Bendixson Rank of the Ziegler Spectrum Over a Commutative Valuation Domain
Authors: Puninski Gennadi
Published: May 2006

We calculate the Cantor-Bendixson rank of the Ziegler spectrum over a commutative valuation domain R proving that it is equal to the double Krull dimension of R.
Notions of locality and their logical characterizations over finite models
Authors: Hella Lauri , Libkin Leonid , Nurmonen Juha
Published: May 2006

Many known tools for proving expressibility bounds for first-ordér logic are based on one of several locality properties. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hanf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of the easiest tools for proving expressibility bounds. These results apply beyond the first-order case. We use them to derive expressibility bounds for first-order logic with unary quantifiers and counting. We also characterize the notions of locality on structures of small degree.
On minimal structures
Authors: Belegradek Oleg V.
Published: May 2006

For any countable transitive complete theory T with infinite models and the finite model property, we construct a minimal structure M such that the theory of M is small if and only if T is small, and is λ-stable if and only if T is λ-stable. This gives a series of new examples of minimal structures.
Initial segments of the lattice of Π10 classes
Authors: Cenzer Douglas , Nies Andre
Published: May 2006

We show that in the lattice of classes there are initial segments [∅, P] = (P) which are not Boolean algebras, but which have a decidable theory. In fact, we will construct for any finite distributive lattice L which satisfies the dual of the usual reduction property a class P such that L is isomorphic to the lattice (P)*, which is (P). modulo finite differences. For the 2-element lattice, we obtain a minimal class, first constructed by Cenzer, Downey, Jockusch and Shore in 1993. For the simplest new class P constructed, P has a single, non-computable limit point and (P)* has three elements, corresponding to ∅, P and a minimal class P0 ⊂ P, The element corresponding to P0 has no complement in the lattice. On the other hand, the theory of (P) is shown to be decidable.

A class P is said to be decidable if it is the set of paths through a computable tree with no dead ends. We show that if P is decidable and has only finitely many limit points, then (P)* is always a Boolean algebra. We show that if P is a decidable class and (P) is not a Boolean algebra, then the theory of (P) interprets the theory of arithmetic and is therefore undecidable.
Partitioning subsets of stable models
Authors: Bays Timothy
Published: May 2006

This paper discusses two combinatorial problems in stability theory. First we prove a partition result for subsets of stable models: for any A and B, we can partition A into ∣B∣<κ(T) pieces. 〈Ai ∣ i < ∣B∣<κ(T)〉. such that for each Ai there is a Bi ⊆ B where ∣Bi∣ < κ(T) and , Second, if A and B are as above and ∣A∣ > ∣B∣, then we try to find A′ ⊂ A and B′ ⊂ B such that ∣A′∣ is as large as possible. ∣B′∣ is as small as possible, and . We prove some positive results in this direction, and we discuss the optimality of these results under ZFC + GCH.
Elementary properties of power series fields over finite fields
Authors: Kuhlmann Franz-Viktor
Published: May 2006

In spite of the analogies between ℚp and which became evident through the work of Ax and Kochen, an adaptation of the complete recursive axiom system given by them for ℚp, to the case of does not render a complete axiom system. We show the independence of elementary properties which express the action of additive polynomials as maps on . We formulate an elementary property expressing this action and show that it holds for all maximal valued fields. We also derive an example of a rather simple immediate valued function field over a henselian defectless ground field which is not a henselian rational function field. This example is of special interest in connection with the open problem of local uniformization in positive characteristic.
Epsilon-logic is more expressive than first-order logic over finite structures
Authors: Otto Martin
Published: May 2006

There are properties of finite structures that are expressible with the use of Hilbert's ∈-operator in a manner that does not depend on the actual interpretation for ∈-terms. but not expressible in plain first-order. This observation strengthens a corresponding result of Gurevich, concerning the invariant use of an auxiliary ordering in first-order logic over finite structures. The present result also implies that certain non-deterministic choice constructs, which have been considered in database theory, properly enhance the expressive power of first-order logic even as far as deterministic queries are concerned, thereby answering a question raised by Abiteboul and Vianu.
Recursive inseparability for residual bounds of finite algebras
Authors: McKenzie Ralph
Published: May 2006

We exhibit a construction which produces for every Turing machine T with two halting states μ0 and μ−1, an algebra B(T) (finite and of finite type) with the property that the variety generated by B(T) is residually large if T halts in state μ−1, while if T halts in state μ0 then this variety is residually bounded by a finite cardinal.
An intuitionistic version of Zermelo's proof that every choice set can be well-ordered
Authors: Wilson J. Todd
Published: May 2006

We give a proof, valid in any elementary topos, of the theorem of Zermelo that any set possessing a choice function for its set of inhabited subsets can be well-ordered. Our proof is considerably simpler than existing proofs in the literature and moreover can be seen as a direct generalization of Zermelo's own 1908 proof of his theorem.
An axiomatics for nonstandard set theory, based on von Neumann–Bernays–Gödel Theory
Authors: Andreev P. V. , Gordon E. I.
Published: May 2006

We present an axiomatic framework for nonstandard analysis—the Nonstandard Class Theory (NCT) which extends von Neumann–Gödel–Bernays Set Theory (NBG) by adding a unary predicate symbol St to the language of NBG (St(X) means that the class X is standard) and axioms—related to it—analogs of Nelson's idealization, standardization and transfer principles. Those principles are formulated as axioms, rather than axiom schemes, so that NCT is finitely axiomatizable. NCT can be considered as a theory of definable classes of Bounded Set Theory by V. Kanovei and M. Reeken. In many aspects NCT resembles the Alternative Set Theory by P. Vopenka. For example there exist semisets (proper subclasses of sets) in NCT and it can be proved that a set has a standard finite cardinality iff it does not contain any proper subsemiset. Semisets can be considered as external classes in NCT. Thus the saturation principle can be formalized in NCT.
The mean value theorem in second order arithmetic
Authors: Hardin Christopher S. , Velleman Daniel J.
Published: May 2006

This paper is a contribution to the project of determining which set existence axioms are needed to prove various theorems of analysis. For more on this project and its history we refer the reader to [1] and [2].

We work in a weak subsystem of second order arithmetic. The language of second order arithmetic includes the symbols 0, 1, =, <, +, ·, and ∈, together with number variables x, y, z, … (which are intended to stand for natural numbers), set variables X, Y, Z, … (which are intended to stand for sets of natural numbers), and the usual quantifiers (which can be applied to both kinds of variables) and logical connectives. We write ∀x < t φ and ∃x < t φ as abbreviations for ∀x(x < t → φ) and ∃x{x < t ∧ φ) respectively; these are called bounded quantifiers. A formula is said to be if it has no quantifiers applied to set variables, and all quantifiers applied to number variables are bounded. It is if it has the form ∃xθ and it is if it has the form ∀xθ, where in both cases θ is .

The theory RCA0 has as axioms the usual Peano axioms, with the induction scheme restricted to formulas, and in addition the comprehension scheme, which consists of all formulas of the form

where φ is , ψ is , and X does not occur free in φ(n). (“RCA” stands for “Recursive Comprehension Axiom.” The reason for the name is that the comprehension scheme is only strong enough to prove the existence of recursive sets.) It is known that this theory is strong enough to allow the development of many of the basic properties of the real numbers, but that certain theorems of elementary analysis are not provable in this theory. Most relevant for our purposes is the fact that it is impossible to prove in RCA0 that every continuous function on the closed interval [0, 1] attains maximum and minimum values (see [1]).

Since the most common proof of the Mean Value Theorem makes use of this theorem, it might be thought that the Mean Value Theorem would also not be provable in RCA0. However, we show in this paper that the Mean Value Theorem can be proven in RCA0. All theorems stated in this paper are theorems of RCA0, and all of our reasoning will take place in RCA0.
Proper forcing and remarkable cardinals II
Authors: Schindler Ralf-Dieter
Published: May 2006

The current paper proves the results announced in [5].

We isolate a new large cardinal concept, “remarkability.” Consistencywise, remarkable cardinals are between ineffable and ω-Erdös cardinals. They are characterized by the existence of “0#-like” embeddings; however, they relativize down to L. It turns out that the existence of a remarkable cardinal is equiconsistent with L(ℝ) absoluteness for proper forcings. In particular, said absoluteness does not imply determinacy.
Ibsen's Political and Social Ideas
Authors: Neserius Philip George
Published: May 2006

Man, “to be himself,” is “to realize himself.” This fundamental thought became a beacon of light which Ibsen unhesitatingly followed through financial distress, through social isolation, and through severe and often malicious criticism by his contemporaries. To advance the country and elevate the people was Ibsen's cardinal aim, which he consistently strove to attain. He dared to be himself; he spoke the truth when he saw it, and fought for his convictions. If one never commits himself, he never expresses himself; his self becomes less and less significant and decisive. Calculating selfishness is the annihilation of self. This was not true of Ibsen. In a letter to Björnson he says: “Had I to decide on an inscription for the monument, I should chose the words: “His life was his best work.” So to conduct one's life as to realize one's self seems to be the brightest attainment possible to a human being. It is the task of one and all of us, but most of us bungle it.”
The Civil Service in the Modern State
Authors: Finer Herman
Published: May 2006

“I'd give them th' votes,” said Mr. Dooley. “But,” he added significantly, “I'd do the countin'!” These words symbolise, in a crude way, the direction of political inquiry in the century prior to the year 1880. Until about that time political scientists were concerned mainly with the processes of policy and law-making. Incident to this were studied things like the nature of public opinion and the electorate, political parties, representative assemblies and their relation to the executive. But the problem of the civil service in the modern state emerged in its full importance not longer than some four decades ago; and indeed, today, we are only in the stage of discovering the questions yet to be explored.

The centre of gravity in political science has plainly shifted from the field of electioneering to that of the civil service. In our own day that machinery serves two purposes of high importance. Firstly, it furnishes the expert knowledge without which parliaments can not, in any adequate fashion, create and enact policies. Secondly, it carries out the commands of the policymaking body. The experience of the United States, of Great Britain, of France, Germany, Canada, Australia and South Africa, shows conclusively that to perform the first of these two functions the members of the representative assemblies have neither the time, the ability, the inclination, nor the machinery. They must come to the permanent office-holders for expert knowledge. And as to the second, a variety of reasons forces them to legislate in general terms and leave the civil servants to draw up statutory rules and orders—to create “secondary legislation,” the enormous and increasing mass of which gives the civil service in the modern state a vast power.
Proportional Representation in Sweden
Authors: Herlitz Nils
Published: May 2006

Fifteen years ago the principle of majority elections became applicable to all phases of public life in Sweden; and along with the movement for democratization there developed the idea of proportional representation. This principle was urged especially by Conservatives, who feared that if elections to Andra Kammaren (the Lower House) should be based upon universal suffrage with the retention of the majority system, the Conservative party would be completely annihilated.
Issues, Candidate Image, and Priming: The Use of Private Polls in Kennedy's 1960 Presidential Campaign
Authors: Jacobs Lawrence R. , Shapiro Robert Y.
Published: May 2006

Interpretations of electoral campaigns have pointed to two mutually exclusive strategies: candidates are expected to focus either on policy issues or on personal image. We argue, however, that social psychologists' notion ofprimingoffers an empirically grounded and theoretically plausible campaign strategy for treating image and issues as interconnected strategic concerns. Based on both quantitative and historical analysis of John F. Kennedy's 1960 presidential campaign, we find that the candidate's policy positions were related to results from his private public opinion polls. Archival and interview evidence suggests that Kennedy deliberately used these popular issues to shape the electorate's standards for evaluating his personal attributes (rather than to win over utility-maximizing voters). We conclude that the study of priming offers one important approach to reintegrating research on candidate strategy and voter behavior.
The Power of the European Parliament as a Conditional Agenda Setter
Authors: Tsebelis George
Published: May 2006

The European Parliament under the currentcooperation procedurehas an important power: it can make proposals that, if accepted by the Commission of the European Communities, are easier for the Council of Ministers to accept than to modify, since only qualified majority is required for acceptance, whereas full unanimity for modification. The importance of this power, which I call the power of theconditional agenda setter, has not been recognized in previous scholarly work. For structural reasons explained in the text, this power is likely to increase in the future. I conclude by arguing that the conditional delegation of power to international actors (the European Parliament, Commission, and the Court of Justice) is a frequent phenomenon in European institutions. This delegation presents three important advantages: it makes possible the selection of one among many possible equilibria, it accelerates European integration, and it diffuses responsibility for politically unpopular measures.
The Evolutionary Stability of Cooperation
Authors: Bendor Jonathan , Swistak Piotr
Published: May 2006

Is cooperation without central authority stable? If so, how robust is it? Despite what might be the conventional wisdom,The Evolution of Cooperationdid not solve this problem deductively. In fact, results obtained later by others seem to have contradicted the book's main message. Reexamining this exceptionally influential work yields a new picture. Part of Axelrod's evolutionary story turns out to be false. But the main intuition, that retaliatory strategies of conditional cooperation are somehow advantaged, proves correct in one specific and significant sense: Under a standard evolutionary dynamic these strategies require the minimal frequency to stabilize. Hence, they support the most robust evolutionary equilibrium: the easiest to reach and retain. Moreover, the less efficient a strategy, the larger is its minimal stabilizing frequency; Hobbesian strategies of pure defection are the least robust. Our main theorems hold for a large class of games that pose diverse cooperation problems: prisoner's dilemma, chicken, stag hunt, and many others.
On the axiom of extensionality, Part II
Authors: Gandy R. O.
Published: May 2006

In this paper it is shown that, if a certain form of Gödel-Bernays set theory which does not include the axiom of extensionality is consistent, then so is the whole system of set theory. The general line of argument is similar to that used in Part I. § 1 describes a reformulation of set theory in which the class-existence axioms are replaced by the use of abstracts. In § 2 some standard theorems, including the theory of the ancestral, are proved without using the axiom of extensionality. In § 3 the appropriate inner model is defined, and the validity in it of the most of the axioms is demonstrated. § 4 deals with the remaining axioms (of infinity and of choice).
Schémas pour le calcul des propositions fondé sur la conjonction et la négation
Authors: Porte Jean
Published: May 2006

On sait que la conjonction et la négation constituent un système de connecteurs suffisant pour formuler le calcul des propositions classiques. Un certain intêrêt s'attache à ces formulations par suite des faits suivants: – les thèses du calcul intuitioniste qui ne comprennent pas d'autres connecteurs que la conjonction et la négation sont identiques aux thèses classiques;

– Lewis ayant formulé ses calculs modaux en prenant la conjonction, la négation et la possibilité comme connecteurs primitifs (voir Lewis-Langford 1932, ch. VI) et ayant été suivi par beaucoup de chercheurs s'occupant de modalités, le calcul classique fondé sur la conjonction et la négation est contenu dans la plupart des systèmes modaux que l'on trouve dans la littérature.

Un système logistique pour le calcul classique fondé sur la conjonction et la négation a été étudié par Rosser (voir Rosser 1953, ch. 4; aussi Copi 1954, ch. 7).

Dans cet article je vais définir cinq autres systèmes logistiques fondés sur les mêmes connecteurs, démontrer leur suffisance (en utilisant les résultats publiés de Rosser et de Copi), et — sauf un cas — démontrer l'indépendance des axiomes de chacun de ces systèmes.
Two theories with axioms built by means of pleonasms
Authors: Ehrenfeucht Andrzej
Published: May 2006

This paper contains examples T1 and T2 of theories which answer the following questions:

(1) Does there exist an essentially undecidable theory with a finite number of non-logical constants which contains a decidable, finitely axiomatizable subtheory?

(2) Does there exist an undecidable theory categorical in an infinite power which has a recursive set of axioms? (Cf. [2] and [3].)

The theory T1 represents a modification of a theory described by Myhill [7]. The common feature of theories T1 and T2 is that in both of them pleonasms are essential in the construction of the axioms.

Let T1 be a theory with identity = which contains one binary predicate R(x, y) and is based on the axioms A1, A2, A3, B1, B2, B3, B4, Cnm which follow.

A1: x = x. A2: x = y ⊃ y = x. A3: x = y ∧ y = z ⊃ x = z.

(Axioms of identity.)

B1: R(x, x). B2: R(x, y) ⊃ R(y, x). B3: R (x, y) ∧ R(y, z) ⊃ R(x, z).

(Axioms of equivalence.)

B4: x = y ⊃ [R(z, x) ≡ R(z,y)].

Let φn be the formula

which express that there is an abstraction class of the relation R which has exactly n elements.

Let f(n) and g(n) be two recursive functions which enumerate two recursively inseparable sets [5], and call these sets X1 and X2.

We now specify the axioms Cmm.

It is obvious that the set composed of the formulas A1−A3, B1−B4, Cnm (n,m = 1,2, …) is recursive.

The theory T1 is essentially undecidable; for if there were a complete and decidable extension T′1 (of it, then the recursive sets Z = {n: φn is provable in T′1} and Z′ = {n: ∼φn is provable in T′1} would separate the sets X1 and X2.
Die nichtaxiomatisierbarkeit des unendlichwertigen Prädikatenkalküls von Łukasiewicz
Authors: Scarpellini Bruno
Published: May 2006

In dieser Arbeit soll eine unendlichwertige Logik untersucht werden, deren Aussagenkalkül von Łukasiewicz und Tarski [3] erstmals diskutiert wurde. Eine ausführliche Darstellung des Prädikatenkalküls findet man in J. D. Rutledge [6] und B. Rosser [5]. Von A. Rose und Rosser wurde die Vollständigkeit des Aussagenkalküls bewiesen [4]. Später wurde von Rutledge die Vollständigkeit des einstelligen Prädikatenkalküls bewiesen, und zwar mit algebraischen Methoden, den sogenannten MV-Algebras, die von C. C. Chang [1] eingeführt worden sind. Hier soll bewiesen werden, dass der volle unendlichwertige Prädikatenkalkül nicht axiomatisierbar ist. Genauer: es soll gezeigt werden, dass die Menge der wahren Formeln, d.h. derjenigen Formeln, die immer den Wert Eins annehmen, nicht rekursiv auf zählbar ist.
Independence proofs in predicate logic with infinitely long expressions
Authors: Karp Carol R.
Published: May 2006

The systems of predicate logic considered here are extensions of ordinary first-order predicate logic. They were obtained by first admitting infinite conjunctions, disjunctions, and quantifications into formulas, and then adjusting the axiom schemata and rules of inference to accommodate them. In this paper, only systems with formulas of denumerable length and “formal proofs” with denumerably many steps will be discussed, though such restrictions are hardly essential. The systems with denumerable conjunctions and disjunctions, but finite quantifications, are semantically complete; i.e., valid formulas are provable. However, systems in which denumerably infinite quantifications are also allowed, are semantically incomplete.
A problem of Rosser and Turquette
Authors: Margaris Angelo
Published: May 2006

In this paper an affirmative solution is given for the following problem in many-valued logic posed by Rosser and Turquette in [6] p. 110:

For every triple ‹s, t, m› with 1 ≤ s < t < m, is it possible to define a system of m-valued logic which satisfies the following conditions? I. Every statement which always takes values ≦ s is provable. II. No statement which ever takes a value > t is provable. III. Of those statements which always take values ≤ t and sometimes take a value > s, some are provable and some are not.

We state now, temporarily deferring comment, a more demanding alternative to Condition III: III′. For every truth value k such that s < k ≦ t, there are statements P and Q such that each takes the value k at least once, but never takes a value > k, and P is provable and Q is not.

In § 2 a solution is given on the level of the statement calculus. The remainder of the present section is devoted to some negative results which serve to clarify the problem, and one positive result which shall cause us to replace Condition III by III′. We confine our attention to the statement calculus.
The semantics of singular terms
Authors: Matheson Gordon
Published: May 2006

There is a distinction within the natural language between those singular terms which designate and those which do not. On the basis of this distinction there arise irregularities both in the assignment to expressions of semantical properties and relations and in the presumed attribution of existence to individuals. Although such irregularities are characteristic of the employment of singular terms, they are not reproduced either for or within the usual formalized languages. Accordingly, we construct a formalized language for which the mentioned irregularities are reproduced — hence, a language which in this respect mirrors more faithfully than is customary the structure of the natural language.
On requirements for conditional probability functions
Authors: Leblanc Hugues
Published: May 2006

Let the prepositional calculus (PC) be cast in the following form: (a) The primitive signs of PC are to be a denumerably infinite hst of propositional letters, the two connectives ‘∼’ and ‘&’, and the two parentheses ‘(‘and’)’; (b) The formulas of PC, referred to hereafter by ‘A’, ‘B’, ‘C’, and ‘D,’ are to be all finite sequences of primitive signs of PC; (c) The well-formed formulas (wffs) of PC are to be all propositional letters, all formulas of the form ∼A, where A is a wff of PC, and all formulas of the form (A&B), where A and B are wffs of PC; (d) (A⊃B) is to be short for ∼(A&∼B), (AνB) short for ∼(∼A&∼B), and (A ≡ B) short for (((A ⊃B)&(B⊃A)).
Short‐term retention of actin filament binding proteins on lamellipodial actin bundles
Authors: Nakagawa Hiroyuki , Terasaki Asako G. , Suzuki Hiroshi , Ohashi Kazuyo , Miyamoto Shigeaki
Published: May 2006

Actin filaments are organised into sub‐compartments of meshwork and bundles in lamellipodia. Localisation of fascin, the LIM and SH3 domain protein 1 (lasp‐1), and lasp‐2 to the bundles suggest their involvement in that organisation; however, their contributions remain unclear. We have compared the turnover of these proteins with actin at the bundle. After photobleaching, EGFP‐actin recovered inwards from the bundle tip, consistent with the retrograde flow by treadmilling. In contrast, the recovery of EGFP‐fascin, ‐lasp‐1 and ‐lasp‐2 occurred from the anterograde direction. These results suggest that these molecules would participate in the stabilisation of bundles but not in initiation.
CO signatures in subtropical convective clouds and anvils during CRYSTAL‐FACE: An analysis of convective transport and entrainment using observations and a cloud‐resolving model
Authors: Lopez Jimena P. , Fridlind Ann M. , Jost Hans‐Jürg , Loewenstein Max , Ackerman Andrew S. , Campos Teresa L. , Weinstock Elliot M. , Sayres David S. , Smith Jessica B. , Pittman Jasna V. , Hallar A. Gannet , Avallone Linnea M. , Davis Sean M. , Herman Robert L.
Published: May 2006

Convective systems are an important mechanism in the transport of boundary layer air into the upper troposphere. The Cirrus Regional Study of Tropical Anvils and Cirrus Layers–Florida Area Cirrus Experiment (CRYSTAL‐FACE) campaign, in July 2002, was developed as a comprehensive atmospheric mission to improve knowledge of subtropical cirrus systems and their roles in regional and global climate. In situ measurements of carbon monoxide (CO), water vapor (H2Ov), and total water (H2Ot) aboard NASA's WB‐57F aircraft and CO aboard the U.S. Navy's Twin Otter aircraft were obtained to study the role of convective transport. Three flights sampled convective outflow on 11, 16 and 29 July found varying degrees of CO enhancement relative to the free troposphere. A cloud‐resolving model used the in situ observations and meteorological fields to study these three systems. Several methods of filtering the observations were devised here using ice water content, relative humidity with respect to ice, and particle number concentration as a means to statistically sample the model results to represent the flight tracks. A weighted histogram based on ice water content observations was then used to sample the simulations for the three flights. In addition, because the observations occurred in the convective outflow cirrus and not in the storm cores, the model was used to estimate the maximum CO within the convective systems. In general, anvil‐level air parcels contained an estimated 20–40% boundary layer air in the analyzed storms.
Nonlinear structures, spectral features, and correlations in a nearly incompressible hydrodynamic fluid
Authors: Shaikh Dastgeer , Zank Gary P.
Published: May 2006

Turbulence simulations of a hydrodynamic fluid are performed to explore various nonlinear aspects of a nearly incompressible (NI) fluid in a regime where temperature fluctuations dominate. The NI model was developed primarily to understand weak compressive effects in interplanetary and interstellar media. Nonlinear structures generated by turbulent relaxation are shown to exist in our two-dimensional fluid simulations. Dynamically weak compressive effects are associated with passively convected thermal fluctuations which enhance the rate of selective decay in decaying NI turbulence. Turbulent relaxation leads to self-organization in thermally dominated NI velocity fluctuations and predicts the formation of large-scale steady-state coherent structures via an inverse cascade mechanism. In agreement with theoretical predictions, density fluctuations are slaved to the incompressible velocity fluctuations and exhibit a Kolmogorov-type power law. Thermal and density fluctuations are found to be anticorrelated in an adiabatic fluid. This suggests that a large fraction of the high plasma-β fluid departs from a thermal equilibrium. Furthermore, compressional effects in nearly incompressible turbulence enhance decay rates significantly and lead to the formation of coherent vortices on much faster time scales when compared with incompressible turbulence.