Submission date: 29 September 2021

Abstract:

We present applications of C_p-theory, the branch of general topology concerned with spaces of real-valued continuous functions, to model theory, mostly in the context of continuous logics. We include C_p-theoretic results and proofs in a self-contained way for model theorists who are not familiar with the techniques of this field. We further generalize some results of Casazza and Iovino, and of the authors, involving the definability of Banach spaces including isomorphic copies of c_0 or ℓ^p, after a problem posed by Odell and Gowers.

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Full text arXiv 2109.14513: pdf, ps.