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

2013/04/30 by Christopher J. Eagle · 1 citation
Mathematics · #math.LO

paper · pdf · doi:10.1016/j.apal.2013.11.006

published as Annals of Pure and Applied Logic 165 (2014) pp. 913-932 · 22 pages

arxiv created 2019/05/30 · arxiv updated 2019/05/31

Abstract

We describe an infinitary logic for metric structures which is analogous to L_{ω1, 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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• Continuous first-order logic of abstract harmonic spaces

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