Journal of Mathematical Logic

ISSNs: 0219-0613, 1793-6691

13 found

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  1.  31
    On ω-strongly measurable cardinals in ℙmax extensions.Navin Aksornthong, Takehiko Gappo, James Holland & Grigor Sargsyan - 2025 - Journal of Mathematical Logic 25 (2).
    We show that in the [Formula: see text] extension of a certain Chang-type model of determinacy, if [Formula: see text], then the restriction of the club filter on [Formula: see text] to [Formula: see text] is an ultrafilter in [Formula: see text]. This answers Question 4.11 of [O. Ben-Neria and Y. Hayut, On [Formula: see text]-strongly measurable cardinals, Forum Math. Sigma 11 (2023) e19].
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  2.  24
    The descriptive complexity of the set of Poisson generic numbers.Verónica Becher, Stephen Jackson, Dominik Kwietniak & Bill Mance - 2025 - Journal of Mathematical Logic 25 (2).
    Let [Formula: see text] be an integer. We show that the set of real numbers that are Poisson generic in base b is [Formula: see text]-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base b and not Poisson generic in base b is complete for the class given by the differences between [Formula: see text] sets. We also show that the effective versions of these results hold (...)
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  3.  28
    Non-Galvin filters.Tom Benhamou, Shimon Garti, Moti Gitik & Alejandro Poveda - 2025 - Journal of Mathematical Logic 25 (2).
    We address the question of consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions [Benhamou and Gitik, Ann. Pure Appl. Logic 173 (2022) 103107; Questions 7.8, 7.9], [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Question 5] and improve theorem [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Theorem 2.3].
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  4.  19
    Rings of finite Morley rank without the canonical base property.Michael Loesch & Daniel Palacín - 2025 - Journal of Mathematical Logic 25 (2).
    We present numerous natural algebraic examples without the so-called Canonical Base Property (CBP). We prove that every commutative unitary ring of finite Morley rank without finite-index proper ideals satisfies the CBP if and only if it is a field, a ring of positive characteristic or a finite direct product of these. In addition, we construct a CM-trivial commutative local ring with a finite residue field without the CBP. Furthermore, we also show that finite-dimensional non-associative algebras over an algebraically closed field (...)
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  5.  21
    Martin’s conjecture for regressive functions on the hyperarithmetic degrees.Patrick Lutz - 2025 - Journal of Mathematical Logic 25 (2).
    We answer a question of Slaman and Steel by showing that a version of Martin’s conjecture holds for all regressive functions on the hyperarithmetic degrees. A key step in our proof, which may have applications to other cases of Martin’s conjecture, consists of showing that we can always reduce to the case of a continuous function.
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  6.  14
    The mouse set theorem just past projective.Mitch Rudominer - 2025 - Journal of Mathematical Logic 25 (2).
    We identify a particular mouse, [Formula: see text], the minimal ladder mouse, that sits in the mouse order just past [Formula: see text] for all n, and we show that [Formula: see text], the set of reals that are [Formula: see text] in a countable ordinal. Thus [Formula: see text] is a mouse set. This is analogous to the fact that [Formula: see text] where [Formula: see text] is the sharp for the minimal inner model with a Woodin cardinal, and (...)
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  7.  11
    On the consistency of ZF with an elementary embedding from Vλ+2 into Vλ+2.Farmer Schlutzenberg - 2025 - Journal of Mathematical Logic 25 (2).
    According to a theorem due to Kenneth Kunen, under ZFC, there is no ordinal [Formula: see text] and nontrivial elementary embedding [Formula: see text]. His proof relied on the Axiom of Choice (AC), and no proof from ZF alone is has been discovered. [Formula: see text] is the assertion, introduced by Hugh Woodin, that [Formula: see text] is an ordinal and there is an elementary embedding [Formula: see text] with critical point [Formula: see text]. And [Formula: see text] asserts that (...)
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  8.  28
    Preservation of NATP.Jinhoo Ahn, Joonhee Kim, Hyoyoon Lee & Junguk Lee - 2025 - Journal of Mathematical Logic 25 (1).
    We prove the preservation theorems for NATP; many of them extend the previously established preservation results for other model-theoretic tree properties. Using them, we also furnish proper examples of NATP theories which are simultaneously TP2 and SOP. First, we show that NATP is preserved by the parametrization and sum of the theories of Fraïssé limits of Fraïssé classes satisfying strong amalgamation property. Second, the preservation of NATP for two kinds of dense/co-dense expansions, i.e. the theories of lovely pairs and of (...)
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  9.  40
    Halin’s infinite ray theorems: Complexity and reverse mathematics.James S. Barnes, Jun Le Goh & Richard A. Shore - 2025 - Journal of Mathematical Logic 25 (1).
    Halin in 1965 proved that if a graph has n many pairwise disjoint rays for each n then it has infinitely many pairwise disjoint rays. We analyze the complexity of this and other similar results in terms of computable and proof theoretic complexity. The statement of Halin’s theorem and the construction proving it seem very much like standard versions of compactness arguments such as König’s Lemma. Those results, while not computable, are relatively simple. They only use arithmetic procedures or, equivalently, (...)
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  10.  30
    Enriching a predicate and tame expansions of the integers.Gabriel Conant, Christian D’Elbée, Yatir Halevi, Léo Jimenez & Silvain Rideau-Kikuchi - 2025 - Journal of Mathematical Logic 25 (1).
    Given a structure [Formula: see text] and a stably embedded [Formula: see text]-definable set Q, we prove tameness preservation results when enriching the induced structure on Q by some further structure [Formula: see text]. In particular, we show that if [Formula: see text] and [Formula: see text] are stable (respectively, superstable, [Formula: see text]-stable), then so is the theory [Formula: see text] of the enrichment of [Formula: see text] by [Formula: see text]. Assuming simplicity of T, elimination of hyperimaginaries and (...)
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  11.  24
    Turing independence and Baire category.Ashutosh Kumar & Saharon Shelah - 2025 - Journal of Mathematical Logic 25 (1).
    We show that it is relatively consistent with ZFC that there is a non-meager set of reals X such that for every non-meager [Formula: see text], there exist distinct [Formula: see text] such that z is computable from the Turing join of x and y.
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  12.  38
    The Biggest Five of Reverse Mathematics.Dag Normann & Sam Sanders - 2025 - Journal of Mathematical Logic 25 (1).
    The aim of Reverse Mathematics (RM for short) is to find the minimal axioms needed to prove a given theorem of ordinary mathematics. These minimal axioms are almost always equivalent to the theorem, working over the base theory of RM, a weak system of computable mathematics. The Big Five phenomenon of RM is the observation that a large number of theorems from ordinary mathematics are either provable in the base theory or equivalent to one of only four systems; these five (...)
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  13.  24
    How far is almost strong compactness from strong compactness.Zhixing You & Jiachen Yuan - 2025 - Journal of Mathematical Logic 25 (1).
    Bagaria and Magidor introduced the notion of almost strong compactness, which is very close to the notion of strong compactness. Boney and Brooke-Taylor asked whether the least almost strongly compact cardinal is strongly compact. Goldberg gives a positive answer in the case [Formula: see text] holds from below and the least almost strongly compact cardinal has uncountable cofinality. In this paper, we give a negative answer for the general case. Our result also gives an affirmative answer to a question of (...)
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