bluuebunny/crossref_metadata_2025_split huggingface dataset:
Simulating polyadic modal logics by monadic ones
Authors: Goguadze George , Piazza Carla , Venema Yde 
Published: March 2005

AbstractWe define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic Λsim in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/recursive axiomatizability, frame completeness and the finite model property, canonicity and first-order definability.
Constructive interpolation in hybrid logic
Authors: Blackburn Patrick , Marx Maarten 
Published: March 2005

AbstractCraig's interpolation lemma (if φ → ψ is valid, then φ → θ and θ → ψ are valid, for θ a formula constructed using only primitive symbols which occur both in φ and ψ) fails for many propositional and first order modal logics. The interpolation property is often regarded as a sign of well-matched syntax and semantics. Hybrid logicians claim that modal logic is missing important syntactic machinery, namely tools for referring to worlds, and that adding such machinery solves many technical problems. The paper presents strong evidence for this claim by defining interpolation algorithms for both propositional and first order hybrid logic. These algorithms produce interpolants for the hybrid logic of every elementary class of frames satisfying the property that a frame is in the class if and only if all its point-generated subframes are in the class. In addition, on the class of all frames, the basic algorithm is conservative: on purely modal input it computes interpolants in which the hybrid syntactic machinery does not occur.
A Gitik iteration with nearly Easton factoring
Authors: Mitchell William J. 
Published: March 2005

AbstractWe reprove Gitik's theorem that if the GCH holds and o(κ) = κ + 1 then there is a generic extension in which κ is still measurable and there is a closed unbounded subset C of κ such that every ν ∈ C is inaccessible in the ground model.Unlike the forcing used by Gitik, the iterated forcing ℛλ+1 used in this paper has the property that if λ is a cardinal less then κ then ℛλ+1 can be factored in V as ℛκ+1 = ℛλ+1 × ℛλ+1,κ where ∣ℛλ+1∣ ≤ λ+ and ℛλ+1,κ does not add any new subsets of λ.
A simple maximality principle
Authors: Hamkins Joel David 
Published: March 2005

AbstractIn this paper, following an idea of Christophe Chalons, I propose a new kind of forcing axiom, the Maximality Principle, which asserts that any sentence φ holding in some forcing extension Vℙ and all subsequent extensions Vℙ*ℚ holds already in V. It follows, in fact, that such sentences must also hold in all forcing extensions of V. In modal terms, therefore, the Maximality Principle is expressed by the scheme (◊ □ φ) ⇒ □ φ, and is equivalent to the modal theory S5. In this article, I prove that the Maximality Principle is relatively consistent with ZFC. A boldface version of the Maximality Principle, obtained by allowing real parameters to appear in φ, is equiconsistent with the scheme asserting that Vδ ≺ V for an inaccessible cardinal δ, which in turn is equiconsistent with the scheme asserting that ORD is Mahlo. The strongest principle along these lines is □ , which asserts that holds in V and all forcing extensions. From this, it follows that 0# exists, that x# exists for every set x, that projective truth is invariant by forcing, that Woodin cardinals are consistent and much more. Many open questions remain.
Approachability and Games on Posets
Authors: Yoshinobu Yasuo 
Published: March 2005

AbstractWe show that for any infinite cardinal κ, every strongly (κ + 1 )-strategically closed poset is strongly κ+-strategically closed if and only if APκ (the approachability property) holds, answering the question asked in [5]. We also give a complete classification of strengths of strategic closure properties and that of strong strategic closure properties respectively.
The non-compactness of square
Authors: Cummings James , Foreman Matthew , Magidor Menachem 
Published: March 2005

This note proves two theorems. The first is that it is consistent to have for every n, but not have . This is done by carefully collapsing a supercompact cardinal and adding square sequences to each ωn. The crux of the proof is that in the resulting model every stationary subset of ℵω+1 ⋂ cof(ω) reflects to an ordinal of cofinality ω1, that is to say it has stationary intersection with such an ordinal.This result contrasts with compactness properties of square shown in [3]. In that paper it is shown that if one has square at every ωn, then there is a square type sequence on the points of cofinality ωk, k > 1 in ℵω+1. In particular at points of cofinality greater than ω1 there is a strongly non-reflecting stationary set of points of countable cofinality.The second result answers a question of Džamonja, by showing that there can be no squarelike sequence above a supercompact cardinal, where “squarelike” means that one replaces the requirement that the cofinal sets be closed and unbounded by the requirement that they be stationary at all points of uncountable cofinality.
Automorphism groups of trivial strongly minimal structures
Authors: Blossier Thomas 
Published: March 2005

AbstractWe study automorphism groups of trivial strongly minimal structures. First we give a characterization of structures of bounded valency through their groups of automorphisms. Then we characterize the triplets of groups which can be realized as the automorphism group of a non algebraic component, the subgroup stabilizer of a point and the subgroup of strong automorphisms in a trivial strongly minimal structure, and also we give a reconstruction result. Finally, using HNN extensions we show that any profinite group can be realized as the stabilizer of a point in a strongly minimal structure of bounded valency.
Exactly controlling the non-supercompact strongly compact cardinals
Authors: Apter Arthur W. , Hamkins Joel David 
Published: March 2005

AbstractWe summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals are supercompact and which are only strongly compact in a forcing extension. Depending upon the method, the surviving non-supercompact strongly compact cardinals can be strong cardinals, have trivial Mitchell rank or even contain a club disjoint from the set of measurable cardinals. These results improve and unify Theorems 1 and 2 of [5], due to the first author.
On revision operators
Authors: Welch P. D. 
Published: March 2005

AbstractWe look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise therevision theoretically definablesubsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta's theory of truth over arithmetic usingfullyvaried revision sequences yields a complete Σ31set of integers; (iii) the set ofstably categoricalsentences using their revision operator Ψ is similarly Σ31and which is complete in GÖdel's universe of constructive setsL; (iv) give an alternative account of a theory of truth—realistic variancethat simplifies full variance, whilst at the same time arriving at Kripkean fixed points.
Canonical functions, non-regular ultrafilters and Ulam's problem on ω1
Authors: Deiser Oliver , Donder Dieter 
Published: March 2005

AbstractOur main results are:Theorem 1. Con(ZFC + “every function f: ω1 → ω1 is dominated by a canonical function”) implies Con(ZFC + “there exists an inaccessible limit of measurable cardinals”). [In fact equiconsistency holds.]Theorem 3. Con(ZFC + “there exists a non-regular uniform ultrafilter on ω1”) implies Con(ZFC + “there exists an inaccessible stationary limit of measurable cardinals”).Theorem 5. Con (ZFC + “there exists an ω1-sequence of ω1-complete uniform filters on ω1 s.t. every A ⊆ ω1 is measurable w.r.t. a filter in (Ulam property)”) implies Con(ZFC + “there exists an inaccessible stationary limit of measurable cardinals”).We start with a discussion of the canonical functions and look at some combinatorial principles. Assuming the domination property of Theorem 1, we use the Ketonen diagram to show that ω2V is a limit of measurable cardinals in Jensen's core model KMO for measures of order zero. Using related arguments we show that ω2V is a stationary limit of measurable cardinals in KMO, if there exists a weakly normal ultrafilter on ω1. The proof yields some other results, e.g., on the consistency strength of weak*-saturated filters on ω1, which are of interest in view of the classical Ulam problem.
Generality of proofs and its Brauerian representation
Authors: Došen Kosta , Petrić Zoran 
Published: March 2005

AbstractThe generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation if and only if they must remain occurrences of the same variable in every generalization of the derivation. The variables in question are propositional or of another type. A generalization of the derivation consists in diversifying variables without changing the rules of inference.This paper examines in the setting of categorial proof theory the conjecture that two derivations with the same premises and conclusions stand for the same proof if and only if they have the same generality. For that purpose generality is defined within a category whose arrows are equivalence relations on finite ordinals, where composition is rather complicated. Several examples are given of deductive systems of derivations covering fragments of logic, with the associated map into the category of equivalence relations of generality.This category is isomorphically represented in the category whose arrows are binary relations between finite ordinals, where composition is the usual simple composition of relations. This representation is related to a classical representation result of Richard Brauer.
The completeness of Heyting first-order logic
Authors: Tait W. W. 
Published: March 2005

AbstractRestricted to first-order formulas, the rules of inference in the Curry-Howard type theory are equivalent to those of first-order predicate logic as formalized by Heyting, with one exception: ∃-elimination in the Curry-Howard theory, where ∃x:A,F(x) is understood as disjoint union, are the projections, and these do not preserve first-orderedness. This note shows, however, that the Curry-Howard theory is conservative over Heyting's system.
Ultrafilters on the natural numbers
Authors: Barney Christopher 
Published: March 2005

AbstractWe study the problem of existence and generic existence of ultrafilters onω. We prove a conjecture of Jörg Brendle's showing that there is an ultrafilter that is countably closed but is not an ordinal ultrafilter under CH. We also show that Canjar's previous partial characterization of the generic existence of Q-points is the best that can be done. More simply put, there is no normal cardinal invariant equality that fully characterizes the generic existence of Q-points. We then sharpen results on generic existence with the introduction ofσ-compact ultrafilters. We show that the generic existence of said ultrafilters is equivalent to. This result, taken along with our result that there exists aKσ, non-countably closed ultrafilter under CH, expands the size of the class of ultrafilters that were known to fit this description before. From the core of the proof, we get a new result on the cardinal invariants of the continuum, i.e., the cofinality of the sets withσ-compact closure is.
Transfer methods for o-minimal topology
Authors: Berarducci Alessandro , Otero Margarita 
Published: March 2005

AbstractLetMbe an o-minimal expansion of an ordered field. Letφbe a formula in the language of ordered domains. In this note we establish some topological properties which are transferred fromφMtoφRand vice versa. Then, we apply these transfer results to give a new proof of a result ofM. Edmundo—based on the work of A. Strzebonski—showing the existence of torsion points in any definably compact group defined in an o-minimal expansion of an ordered field.
Expansions of geometries
Authors: Baldwin John T. 
Published: March 2005

AbstractFor n < ω, expand the structure (n, S, I, F) (with S the successor relation, I, F as the initial and final element) by forming graphs with edge probability n−α for irrational α, with 0 < α < 1. The sentences in the expanded language, which have limit probability 1, form a complete and stable theory.
Fat sets and saturated ideals
Authors: Krueger John 
Published: March 2005

AbstractWe strengthen a theorem of Gitik and Shelah [6] by showing that if κ is either weakly inaccessible or the successor of a singular cardinal andSis a stationary subset of κ such thatNSκ↾Sis saturated then κ ∖Sis fat. Using this theorem we derive some results about the existence of fat stationary sets. We then strengthen some results due to Baumgartner and Taylor [2], showing in particular that ifIis aλ+++-saturated normal ideal onPκλthen the conditions of beingλ+-preserving, weakly presaturated, and presaturated are equivalent forI.
Non-well-foundedness of well-orderable power sets
Authors: Forster T. E. , Truss J. K. 
Published: March 2005

AbstractTarski [5] showed that for any setX, its setω(X) of well-orderable subsets has cardinality strictly greater than that ofX, even in the absence of the axiom of choice. We construct a Fraenkel-Mostowski model in which there is an infinite strictly descending sequence under the relation ∣ω(X)∣ = ∣Y∣. This contrasts with the corresponding situation for power sets, where use of Hartogs' ℵ-function easily establishes that there can be no infinite descending sequence under the relation.
The approximation structure of a computably approximable real
Authors: Barmpalias George 
Published: March 2005

AbstractA new approach for a uniform classification of the computably approximable real numbers is introduced. This is an important class of reals, consisting of the limits of computable sequences of rationals, and it coincides with the 0′-computable reals. Unlike some of the existing approaches, this applies uniformly to all reals in this class: to each computably approximable real x we assign a degree structure, the structure of all possible ways available to approximate x. So the main criterion for such classification is the variety of the effective ways we have to approximate a real number. We exhibit extreme cases of such approximation structures and prove a number of related results.
Differential forms in the model theory of differential fields
Authors: Pierce David 
Published: March 2005

AbstractFields of characteristic zero with several commuting derivations can be treated as fields equipped with aspaceof derivations that is closed under the Lie bracket. The existentially closed instances of such structures can then be given a coordinate-free characterization in terms of differential forms. The main tool for doing this is a generalization of the Frobenius Theorem of differential geometry.
Elementary properties of the Boolean hull and reduced quotient functors
Authors: Dickmann M. A. , Miraglia F. 
Published: March 2005

In [12] we proved the following isotropy-reflection principle:Theorem. Let F be a formally real field and let Fp denote its Pythagorean closure. The natural embedding of reduced special groups from Gred(F) into Gred(Fp) = G(FP) induced by the inclusion of fields, reflects isotropy.Here Gred(F) denotes the reduced special group (with underlying group Ḟ/ΣḞ2) associated to the field F, henceforth assumed formally real; cf. [11], Chapter 1, §3, for details.The result proved in [12] is, in fact, more general. For example, the Pythagorean closure Fp can be replaced in the statement above by the intersection of all real closures of F (inside a fixed algebraic closure). Similar statements hold, more generally, for all relative Pythagorean closures of F in the sense of Becker [3], Chapter II, §3.Since the notion of isotropy of a quadratic form can be expressed by a first-order formula in the natural language LSG for special groups (with the coefficients as parameters), this result raises the question whether the embedding ιFFp: Gred(F) ↪ G (Fp) is elementary. Further, since the LSG-formula expressing isotropy is positive-existential, one may also ask whether ιFFp reflects all (closed) formulas ofthat kind with parameters in Gred(F).In this paper we give a negative answer to the first of these questions, for a vast class of formally real (non-Pythagorean) fields F (Prop. 5.1). This follows from rather general preservation results concerning the “Boolean hull” and the “reduced quotient” operations on special groups.
A hierarchy for the plus cupping Turing degrees
Authors: Wang Yong , Li Angsheng 
Published: March 2005

AbstractWe say that a computably enumerable (c. e.) degree a is plus-cupping, if for every c.e. degree x with 0 < x ≤ a, there is a c. e. degree y ≠ 0′ such that x ∨ y = 0′. We say that a is n-plus-cupping, if for every c. e. degree x, if 0 < x ≤ a, then there is a lown c. e. degree I such that x ∨ I = 0′. Let PC and PCn be the set of all plus-cupping, and n-plus-cupping c. e. degrees respectively. Then PC1 ⊆ PC2 ⊆ PC3 = PC. In this paper we show that PC1 ⊂ PC2, so giving a nontrivial hierarchy for the plus cupping degrees. The theorem also extends the result of Li, Wu and Zhang [14] showing that LC1 ⊂ LC2, as well as extending the Harrington plus-cupping theorem [8].
Embedding jump upper semilattices into the Turing degrees
Authors: Montalbán Antonio 
Published: March 2005

AbstractWe prove that every countable jump upper semilattice can be embedded in, where a jump upper semilattice (jusl) is an upper semilattice endowed with a strictly increasing and monotone unary operator that we call jump, andis the jusl of Turing degrees. As a corollary we get that the existential theory of 〈D, ≤T, ∨, ′〉 is decidable. We also prove that this result is not true about jusls with 0, by proving that not every quantifier free 1-type of jusl with 0 is realized in. On the other hand, we show that every quantifier free 1-type of jump partial ordering (jpo) with 0 is realized in. Moreover, we show that if every quantifier free type,p(x1,…,xn), of jpo with 0, which contains the formulax1≤ 0(m)& … &xn≤ 0(m)for somem, is realized in, then every quantifier free type of jpo with 0 is realized in.We also study the question of whether every jusl with the c.p.p. and sizeis embeddable in. We show that forthe answer is no, and that forκ= ℵ1it is independent of ZFC. (It is true if MA(κ) holds.)
Classical and constructive hierarchies in extended intuitionistic analysis
Authors: Moschovakis Joan Rand 
Published: March 2005

AbstractThis paper introduces an extension of Kleene's axiomatization of Brouwer's intuitionistic analysis, in which the classical arithmetical and analytical hierarchies are faithfully represented as hierarchies of the domains of continuity. A domain of continuity is a relation R(α) on Baire space with the property that every constructive partial functional defined on {α: R(α)} is continuous there. The domains of continuity for coincide with the stable relations (those equivalent in to their double negations), while every relation R(α) is equivalent in to ∃βA(α, β) for some stable A(α, β) (which belongs to the classical analytical hierarchy).The logic of is intuitionistic. The axioms of include countable comprehension, bar induction, Troelstra's generalized continuous choice, primitive recursive Markov's Principle and a classical axiom of dependent choices proposed by Krauss. Constructive dependent choices, and constructive and classical countable choice, are theorems, is maximal with respect to classical Kleene function realizability, which establishes its consistency. The usual disjunction and (recursive) existence properties ensure that preserves the constructive sense of “or” and “there exists.”
Isomorphisms of splits of computably enumerable sets
Authors: Cholak Peter A. , Harrington Leo A. 
Published: March 2005

AbstractWe show that if A and are automorphic via Φ then the structures (A) and () are Δ30-isomorphic via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.
Universally Baire sets and definable well-orderings of the reals
Authors: Friedman SY D. , Schindler Ralf 
Published: March 2005

AbstractLet n ≥ 3 be an integer. We show that it is consistent (relative to the consistency of n − 2 strong cardinals) that every Σ1n-set of reals is universally Baire yet there is a (lightface) projective well-ordering of the reals. The proof uses “David's trick” in the presence of inner models with strong cardinals.
A theory for Log-Space and NLIN versus co-NLIN
Authors: Pollett Chris 
Published: March 2005

AbstractThe use of Nepomnjaščiǐ's Theorem in the proofs of independence results for bounded arithmetic theories is investigated. Using this result and similar ideas, it is shown that at least one ofS1orTLSdoes not prove the Matiyasevich-Robinson-Davis-Putnam Theorem. It is also established thatTLSdoes not prove a statement that roughly means nondeterministic linear time is equal to co-nondeterministic linear time. HereS1is a conservative extension of the well-studied theoryIΔ0andTLSis a theory for LOGSPACE reasoning.
Ranked partial structures
Authors: Carlson Timothy J. 
Published: March 2005

AbstractThe theory of ranked partial structures allows a reinterpretation of several of the standard results of model theory and first-order logic and is intended to provide a proof-theoretic method which allows for the intuitions of model theory. A version of the downward Löwenheim-Skolem theorem is central to our development. In this paper we will present the basic theory of ranked partial structures and their logic including an appropriate version of the completeness theorem.
Cardinal-preserving extensions
Authors: Friedman Sy D. 
Published: March 2005

AbstractA classic result of Baumgartner-Harrington-Kleinberg [1] implies that assuming CH a stationary subset of ω1 has a CUB subset in a cardinal-perserving generic extension of V, via a forcing of cardinality ω1. Therefore, assuming that ω2L is countable: {X ∈ L ∣ X ⊆ ω1L and X has a CUB subset in a cardinal-preserving extension of L} is constructive, as it equals the set of constructible subsets of ω1L which in L are stationary. Is there a similar such result for subsets of ω2L? Building on work of M. Stanley [9], we show that there is not. We shall also consider a number of related problems, examining the extent to which they are “solvable” in the above sense, as well as denning a notion of reduction between them.