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  1.  4
    Continuous Higher Randomness.Laurent Bienvenu, Noam Greenberg & Benoit Monin - 2017 - Journal of Mathematical Logic 17 (1):1750004.
    We investigate the role of continuous reductions and continuous relativization in the context of higher randomness. We define a higher analogue of Turing reducibility and show that it interacts well with higher randomness, for example with respect to van Lambalgen’s theorem and the Miller–Yu/Levin theorem. We study lowness for continuous relativization of randomness, and show the equivalence of the higher analogues of the different characterizations of lowness for Martin-Löf randomness. We also characterize computing higher K-trivial sets by higher random sequences. (...)
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  2.  1
    Exact Saturation in Simple and NIP Theories.Itay Kaplan, Saharon Shelah & Pierre Simon - 2017 - Journal of Mathematical Logic 17 (1):1750001.
    A theory T is said to have exact saturation at a singular cardinal κ if it has a κ-saturated model which is not κ+-saturated. We show, under some set-theoretic assumptions, that any simple theory has exact saturation. Also, an NIP theory has exact saturation if and only if it is not distal. This gives a new characterization of distality.
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  3.  1
    Uniformity, Universality, and Computability Theory.Andrew S. Marks - 2017 - Journal of Mathematical Logic 17 (1):1750003.
    We prove a number of results motivated by global questions of uniformity in computabi- lity theory, and universality of countable Borel equivalence relations. Our main technical tool is a game for constructing functions on free products of countable groups. We begin by investigating the notion of uniform universality, first proposed by Montalbán, Reimann and Slaman. This notion is a strengthened form of a countable Borel equivalence relation being universal, which we conjecture is equivalent to the usual notion. With this additional (...)
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  4.  2
    On Definable Galois Groups and the Strong Canonical Base Property.Daniel Palacín & Anand Pillay - 2017 - Journal of Mathematical Logic 17 (1):1750002.
    In [E. Hrushovski, D. Palacín and A. Pillay, On the canonical base property, Selecta Math. 19 865–877], Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that T has the canonical base property in a strong form; “internality to” being replaced by “algebraicity in”. In the current paper, we give a reasonably robust definition of the “strong canonical base property” in a rather more general finite rank context than [E. Hrushovski, D. (...)
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  5.  1
    Corrigendum: The ∀∃ Theory of Peano Σ1 Sentences.V. Yu Shavrukov - 2017 - Journal of Mathematical Logic 17 (1):1792001.
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