Omitting types for infinitary [ 0, 1 ] -valued logic

Annals of Pure and Applied Logic 165 (3):913-932 (2014)
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Abstract

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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Citations of this work

Omitting types in logic of metric structures.Ilijas Farah & Menachem Magidor - 2018 - Journal of Mathematical Logic 18 (2):1850006.
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.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Metamathematics of Fuzzy Logic.Petr Hájek - 1998 - Dordrecht, Boston and London: Kluwer Academic Publishers.
On Fuzzy Logic I Many‐valued rules of inference.Jan Pavelka - 1979 - Mathematical Logic Quarterly 25 (3-6):45-52.
On Fuzzy Logic III. Semantical completeness of some many-valued propositional calculi.Jan Pavelka - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (25-29):447-464.

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