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  1. Encoding Complete Metric Structures by Classical Structures.Nathanael Leedom Ackerman - 2020 - Logica Universalis 14 (4):421-459.
    We show how to encode, by classical structures, both the objects and the morphisms of the category of complete metric spaces and uniformly continuous maps. The result is a category of, what we call, cognate metric spaces and cognate maps. We show this category relativizes to all models of set theory. We extend this encoding to an encoding of complete metric structures by classical structures. This provide us with a general technique for translating results about infinitary logic on classical structures (...)
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  • Continuous Logic and Borel Equivalence Relations.Andreas Hallbäck, Maciej Malicki & Todor Tsankov - 2023 - Journal of Symbolic Logic 88 (4):1725-1752.
    We study the complexity of isomorphism of classes of metric structures using methods from infinitary continuous logic. For Borel classes of locally compact structures, we prove that if the equivalence relation of isomorphism is potentially $\mathbf {\Sigma }^0_2$, then it is essentially countable. We also provide an equivalent model-theoretic condition that is easy to check in practice. This theorem is a common generalization of a result of Hjorth about pseudo-connected metric spaces and a result of Hjorth–Kechris about discrete structures. As (...)
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  • Omitting types in logic of metric structures.Ilijas Farah & Menachem Magidor - 2018 - Journal of Mathematical Logic 18 (2):1850006.
    This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete...
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  • Two applications of topology to model theory.Christopher J. Eagle, Clovis Hamel & Franklin D. Tall - 2021 - Annals of Pure and Applied Logic 172 (5):102907.
    By utilizing the topological concept of pseudocompactness, we simplify and improve a proof of Caicedo, Dueñez, and Iovino concerning Terence Tao's metastability. We also pinpoint the exact relationship between the Omitting Types Theorem and the Baire Category Theorem by developing a machine that turns topological spaces into abstract logics.
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