Showing papers in "Annals of Pure and Applied Logic in 2015"

TL;DR: In this article, the authors show that the generic mantle of V is the intersection of all HODs of all set-forcing extensions of V and the generic HOD is always a model of ZFC.

TL;DR: An algorithm for proving universal statements by induction that separates this problem into two phases, and heavily exploit a correspondence between tree grammars and proofs already applied successfully to the generation of non-analytic cuts in the setting of pure first-order logic.

TL;DR: This paper presents an algorithm for proving the CIP for modal logics by induction on a nested-sequent derivation and is applied to all the logics of the so-called modal cube.

TL;DR: It is shown that if the base domain of the natural numbers is extended with nonstandard elements, then the bounded functional interpretation can be seen as falling out from a functional interpretation of nonstandard number theory without intensional notions.

TL;DR: In this paper, the question of whether a field admits a non-trivial 0-definable p-henselian valuation in the language of rings is investigated.

TL;DR: In this paper, it was shown that first-order consequences of independence logic sentences can be axiomatized and proved that it is complete in this sense, which is a generalization of the result for dependence logic introduced in [15].

TL;DR: Three constructive versions of Tarski's theory have been modified so that the points they assert to exist are unique and depend continuously on parameters, and it is shown that objects proved to exist can be constructed by ruler and compass.

TL;DR: A preservation lemma implicit in Mitchell's PhD thesis is presented, which generalizes all previous versions of Hamkins' Key lemma and a new proof of the ‘superdestructibility’ theorems of Hamkin and Shelah is presented.

TL;DR: In this article, it was shown that for sufficiently large n, SAT is not computable by circuits of size n 4 k c where k ≥ 1, c ≥ 2 unless each function f ∈ SIZE ( n k ) can be approximated by formulas of subexponential size 2 O ( n 1 / c ) with subexponentially advantage.

TL;DR: A version with non-definable forcing notions of Shelah's theory of iterated forcing along a template that, if κ is a measurable cardinal and θ κ μ λ are uncountable regular cardinals, then there is a ccc poset forcing s = θ b = μ a = λ .

TL;DR: This paper builds a dimension theory related to Shelah's 2-rank, dp- rank, and o-minimal dimension, and exhibits the notion of the n -multi-order property, generalizing the order property, and uses this to create op-Rank, which generalizes 2-Rank.

TL;DR: The reverse mathematics of aspects of basic classical and effective model theory, including: existence of homogeneous and saturated models, different type-amalgamation properties, the preorder of models under elementary embeddability, and existence of indiscernibles are examined.

TL;DR: A description of the minimal subflow and Ellis group of the universal definable G ( M ) -flow S G, ext ( M ), which is isomorphic to N G ( H ) ∩ K ( R ) , which extends the result of G.

TL;DR: It is proved that large cardinals need not generally exhibit their large cardinal nature in HOD, and there can be a proper class of supercompact cardinals in V, none of them weakly compact in H OD, with no supercompacts in Hod.

TL;DR: It is shown that if λ is large enough and there are no inner models with fairly large cardinals, then ⋄ κ, λ [ λ + ] holds.

TL;DR: In this article, it was shown that the Erdős-Moser theorem does not admit a universal instance and the stable version of the thin set theorem admits no universal instance.

TL;DR: A new form of Ramsey's Theorem for pairs the authors call the H-closure Theorem, where H stands for “homogeneous”, which is a property of well-founded relations, intuitionistically provable, informative, and simple to use in intuitionistic proofs.

TL;DR: In this article, the authors give an example of a 4-regular infinite automatic graph of intermediate growth, constructed as a Schreier graph of a certain group generated by 3-state automata.

TL;DR: The problem of finding a PA-complete Turing oracle which preserves the strong f-randomness of X while avoiding a Turing cone is studied and it is proved that the cones which cannot always be avoided are precisely the K-trivial ones.

TL;DR: The combined interpretation, seen as a model construction in the sense of Visser's miniature model theory, is a new way of construction for classical theories and could be said the third kind of model construction ever used which is non-trivial on the logical connective level, after generic extension a la Cohen and Krivine's classical realisability model.

TL;DR: In this paper, the structural properties of standard and non-standard models of set theory are exploited to produce automorphisms that are well-behaved along an initial segment of their ordinals.

TL;DR: This work investigates which computable equivalence structures are isomorphic relative to the Halting problem by identifying isomorphic structures that are equivalent to Halting structures.

TL;DR: A lower bound of Feferman's system T 0 of explicit mathematics (but only when formulated on classical logic) with a concrete interpretation of the subsystem Σ 2 1 -AC + ( BI ) of second order arithmetic inside T 0 is given.

TL;DR: It is established that the quantifier alternation hierarchy of formulae of second-order propositional modal logic (SOPML) induces an infinite corresponding semantic hierarchy over the class of finite directed graphs.

TL;DR: A characterization of projective formulas generalizing Ghilardi's characterization in the parameter-free case is given, leading to new proofs of Rybakov's results that admissibility with parameters is decidable and unification is finitary for logics satisfying suitable frame extension properties.

TL;DR: It is shown that RCA 0 ⁎ does make it possible to characterize the natural numbers categorically by means of a set of second-order sentences, and that a certain Π 2 1 -conservative extension of RCA zero admits a provably categorical single-sentence characterization of the naturals.

TL;DR: A depth-first search based algorithm to find the truth value of the root of an AND–OR tree is considered, and it is shown that the maximizer is an independent identical distributions (IID).

TL;DR: Using Neeman's side condition method it is possible to obtain PFA variations and prove consistency results for them, and to outline a portfolio of novel iterable properties of c.

TL;DR: It is shown that one can force a model where 2 ℵ ω is a strong limit cardinal, and the tree property holds at allℵ 2 n, for n > 0 .

TL;DR: In this article, it was shown that if a cardinal is a Ramsey or a strongly Ramsey cardinal and F is a class function on the regular cardinals having a closure point at and obeying the constraints of Easton's theorem, namely, F ( ) F( ) for and < cf(F ( )), then there is a conality preserving forcing extension in which remains Ramsey or strongly Ramsey respectively and 2 = F( ] for every regular cardinal.