Journal of Mathematical Logic

ISSNs: 0219-0613, 1793-6691

19 found

View year:

  1.  12
    Few new reals.David Asperó & Miguel Angel Mota - 2023 - Journal of Mathematical Logic 24 (2).
    We introduce a new method for building models of [Formula: see text], together with [Formula: see text] statements over [Formula: see text], by forcing. Unlike other forcing constructions in the literature, our construction adds new reals, although only [Formula: see text]-many of them. Using this approach, we build a model in which a very strong form of the negation of Club Guessing at [Formula: see text] known as [Formula: see text] holds together with [Formula: see text], thereby answering a well-known (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  2.  10
    Coarse computability, the density metric, Hausdorff distances between Turing degrees, perfect trees, and reverse mathematics.Denis R. Hirschfeldt, Carl G. Jockusch & Paul E. Schupp - 2023 - Journal of Mathematical Logic 24 (2).
    For [Formula: see text], the coarse similarity class of A, denoted by [Formula: see text], is the set of all [Formula: see text] such that the symmetric difference of A and B has asymptotic density 0. There is a natural metric [Formula: see text] on the space [Formula: see text] of coarse similarity classes defined by letting [Formula: see text] be the upper density of the symmetric difference of A and B. We study the metric space of coarse similarity classes (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  3.  14
    Henselian expansions of NIP fields.Franziska Jahnke - 2023 - Journal of Mathematical Logic 24 (2).
    Let K be an NIP field and let v be a Henselian valuation on K. We ask whether [Formula: see text] is NIP as a valued field. By a result of Shelah, we know that if v is externally definable, then [Formula: see text] is NIP. Using the definability of the canonical p-Henselian valuation, we show that whenever the residue field of v is not separably closed, then v is externally definable. In the case of separably closed residue field, we (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  4.  9
    Ramsey’s theorem for pairs, collection, and proof size.Leszek Aleksander Kołodziejczyk, Tin Lok Wong & Keita Yokoyama - 2023 - Journal of Mathematical Logic 24 (2).
    We prove that any proof of a [Formula: see text] sentence in the theory [Formula: see text] can be translated into a proof in [Formula: see text] at the cost of a polynomial increase in size. In fact, the proof in [Formula: see text] can be obtained by a polynomial-time algorithm. On the other hand, [Formula: see text] has nonelementary speedup over the weaker base theory [Formula: see text] for proofs of [Formula: see text] sentences. We also show that for (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  5.  14
    Logical metatheorems for accretive and (generalized) monotone set-valued operators.Nicholas Pischke - 2023 - Journal of Mathematical Logic 24 (2).
    Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of certain set-valued mappings between function spaces. This paper deals with the computational properties of these accretive and (generalized) monotone set-valued operators. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie “non-computational” proofs from the mainstream literature. To this end, we establish logical metatheorems (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6.  7
    Maximal models up to the first measurable in ZFC.John T. Baldwin & Saharon Shelah - 2023 - Journal of Mathematical Logic 24 (1).
    Theorem: There is a complete sentence [Formula: see text] of [Formula: see text] such that [Formula: see text] has maximal models in a set of cardinals [Formula: see text] that is cofinal in the first measurable [Formula: see text] while [Formula: see text] has no maximal models in any [Formula: see text].
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  7.  17
    Higher indescribability and derived topologies.Brent Cody - 2023 - Journal of Mathematical Logic 24 (1).
    We introduce reflection properties of cardinals in which the attributes that reflect are expressible by infinitary formulas whose lengths can be strictly larger than the cardinal under consideration. This kind of generalized reflection principle leads to the definitions of [Formula: see text]-indescribability and [Formula: see text]-indescribability of a cardinal [Formula: see text] for all [Formula: see text]. In this context, universal [Formula: see text] formulas exist, there is a normal ideal associated to [Formula: see text]-indescribability and the notions of [Formula: (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  8.  9
    Hindman’s theorem in the hierarchy of choice principles.David Fernández-Bretón - 2023 - Journal of Mathematical Logic 24 (1).
    In the context of [Formula: see text], we analyze a version of Hindman’s finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the [Formula: see text].
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  9.  16
    Strongly compact cardinals and ordinal definability.Gabriel Goldberg - 2023 - Journal of Mathematical Logic 24 (1).
    This paper explores several topics related to Woodin’s HOD conjecture. We improve the large cardinal hypothesis of Woodin’s HOD dichotomy theorem from an extendible cardinal to a strongly compact cardinal. We show that assuming there is a strongly compact cardinal and the HOD hypothesis holds, there is no elementary embedding from HOD to HOD, settling a question of Woodin. We show that the HOD hypothesis is equivalent to a uniqueness property of elementary embeddings of levels of the cumulative hierarchy. We (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  10.  11
    Exactly two and exactly three near-coherence classes.Heike Mildenberger - 2023 - Journal of Mathematical Logic 24 (1).
    We prove that for [Formula: see text] and [Formula: see text] there is a forcing extension with exactly n near-coherence classes of non-principal ultrafilters. We introduce localized versions of Matet forcing and we develop Ramsey spaces of names. The evaluation of some of the new forcings is based on a relative of Hindman’s theorem due to Blass 1987.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  11.  13
    Covering at limit cardinals of K.William J. Mitchell & Ernest Schimmerling - 2023 - Journal of Mathematical Logic 24 (1).
    Assume that there is no transitive class model of [Formula: see text] with a Woodin cardinal. Let [Formula: see text] be a singular ordinal such that [Formula: see text] and [Formula: see text]. Suppose [Formula: see text] is a regular cardinal in K. Then [Formula: see text] is a measurable cardinal in K. Moreover, if [Formula: see text], then [Formula: see text].
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  12.  19
    Actions of tame abelian product groups.Shaun Allison & Assaf Shani - 2023 - Journal of Mathematical Logic 23 (3).
    A Polish group G is tame if for any continuous action of G, the corresponding orbit equivalence relation is Borel. When [Formula: see text] for countable abelian [Formula: see text], Solecki [Equivalence relations induced by actions of Polish groups, Trans. Amer. Math. Soc. 347 (1995) 4765–4777] gave a characterization for when G is tame. In [L. Ding and S. Gao, Non-archimedean abelian Polish groups and their actions, Adv. Math. 307 (2017) 312–343], Ding and Gao showed that for such G, the (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  13.  12
    More definable combinatorics around the first and second uncountable cardinals.William Chan, Stephen Jackson & Nam Trang - 2023 - Journal of Mathematical Logic 23 (3).
    Assume [Formula: see text]. If [Formula: see text] is an ordinal and X is a set of ordinals, then [Formula: see text] is the collection of order-preserving functions [Formula: see text] which have uniform cofinality [Formula: see text] and discontinuous everywhere. The weak partition properties on [Formula: see text] and [Formula: see text] yield partition measures on [Formula: see text] when [Formula: see text] and [Formula: see text] when [Formula: see text]. The following almost everywhere continuity properties for functions on (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  14.  10
    The degree of nonminimality is at most 2.James Freitag, Rémi Jaoui & Rahim Moosa - 2023 - Journal of Mathematical Logic 23 (3).
    In this paper, it is shown that if [Formula: see text] is a complete type of Lascar rank at least 2, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations [Formula: see text], [Formula: see text] such that p has a nonalgebraic forking extension over [Formula: see text]. Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over [Formula: see text]. The results are (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  15.  12
    Co-theory of sorted profinite groups for PAC structures.Daniel Max Hoffmann & Junguk Lee - 2023 - Journal of Mathematical Logic 23 (3).
    We achieve several results. First, we develop a variant of the theory of absolute Galois groups in the context of many sorted structures. Second, we provide a method for coding absolute Galois groups of structures, so they can be interpreted in some monster model with an additional predicate. Third, we prove the “Weak Independence Theorem” for pseudo-algebraically closed (PAC) substructures of an ambient structure with no finite cover property (nfcp) and the property [Formula: see text]. Fourth, we describe Kim-dividing in (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  16.  16
    Corrigendum to Reducing ω-model reflection to iterated syntactic reflection.Fedor Pakhomov & James Walsh - 2023 - Journal of Mathematical Logic 23 (3).
    We fix a gap in a proof in our paper Reducing ω-model reflection to iterated syntactic reflection.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  17.  16
    Compactness and guessing principles in the Radin extensions.Omer Ben-Neria & Jing Zhang - 2023 - Journal of Mathematical Logic 23 (2).
    We investigate the interaction between compactness principles and guessing principles in the Radin forcing extensions. In particular, we show that in any Radin forcing extension with respect to a measure sequence on [Formula: see text], if [Formula: see text] is weakly compact, then [Formula: see text] holds. This provides contrast with a well-known theorem of Woodin, who showed that in a certain Radin extension over a suitably prepared ground model relative to the existence of large cardinals, the diamond principle fails (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  18.  13
    Invariant measures in simple and in small theories.Artem Chernikov, Ehud Hrushovski, Alex Kruckman, Krzysztof Krupiński, Slavko Moconja, Anand Pillay & Nicholas Ramsey - 2023 - Journal of Mathematical Logic 23 (2).
    We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting of discrete groups (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  19.  40
    The two halves of disjunctive correctness.Cezary Cieśliński, Mateusz Łełyk & Bartosz Wcisło - 2023 - Journal of Mathematical Logic 23 (2).
    Ali Enayat had asked whether two halves of Disjunctive Correctness ([Formula: see text]) for the compositional truth predicate are conservative over Peano Arithmetic (PA). In this paper, we show that the principle “every true disjunction has a true disjunct” is equivalent to bounded induction for the compositional truth predicate and thus it is not conservative. On the other hand, the converse implication “any disjunction with a true disjunct is true” can be conservatively added to [Formula: see text]. The methods introduced (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
 Previous issues
  
Next issues