6 found
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  1.  14
    An undecidable extension of Morley's theorem on the number of countable models.Christopher J. Eagle, Clovis Hamel, Sandra Müller & Franklin D. Tall - 2023 - Annals of Pure and Applied Logic 174 (9):103317.
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  2.  36
    Omitting types for infinitary [ 0, 1 ] -valued logic.Christopher J. Eagle - 2014 - Annals of Pure and Applied Logic 165 (3):913-932.
    We describe an infinitary logic for metric structures which is analogous to Lω1,ω. We show that this logic is capable of expressing several concepts from analysis that cannot be expressed in finitary continuous logic. Using topological methods, we prove an omitting types theorem for countable fragments of our infinitary logic. We use omitting types to prove a two-cardinal theorem, which yields a strengthening of a result of Ben Yaacov and Iovino concerning separable quotients of Banach spaces.
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  3.  25
    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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  4.  16
    Fraïssé Limits of C*-Algebras.Christopher J. Eagle, Ilijas Farah, Bradd Hart, Boris Kadets, Vladyslav Kalashnyk & Martino Lupini - 2016 - Journal of Symbolic Logic 81 (2):755-773.
    We realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite II1factor as Fraïssé limits of suitable classes of structures. Moreover by means of Fraïssé theory we provide new examples of AF algebras with strong homogeneity properties. As a consequence of our analysis we deduce Ramsey-theoretic results about the class of full-matrix algebras.
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  5.  7
    Concrete barriers to quantifier elimination in finite dimensional C*‐algebras.Christopher J. Eagle & Todd Schmid - 2019 - Mathematical Logic Quarterly 65 (4):490-497.
    Work of Eagle, Farah, Goldbring, Kirchberg, and Vignati shows that the only separable C*‐algebras that admit quantifier elimination in continuous logic are,,, and the continuous functions on the Cantor set. We show that, among finite dimensional C*‐algebras, quantifier elimination does hold if the language is expanded to include two new predicate symbols: One for minimal projections, and one for pairs of unitarily conjugate elements. Both of these predicates are definable, but not quantifier‐free definable, in the usual language of C*‐algebras. We (...)
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  6.  15
    Model-Theoretic Properties of Dynamics on the Cantor Set.Christopher J. Eagle & Alan Getz - 2022 - Notre Dame Journal of Formal Logic 63 (3):357-371.
    We examine topological dynamical systems on the Cantor set from the point of view of the continuous model theory of commutative C*-algebras. After some general remarks, we focus our attention on the generic homeomorphism of the Cantor set, as constructed by Akin, Glasner, and Weiss. We show that this homeomorphism is the prime model of its theory. We also show that the notion of “generic” used by Akin, Glasner, and Weiss is distinct from the notion of “generic” encountered in Fraïssé (...)
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