C_p-Theory for Model Theorists

2021/09/29 by Clovis Hamel, Hamel, Clovis, Franklin D. Tall +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge

paper · pdf · doi:10.48550/arxiv.2109.14513

openalex publication_date 2021/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 c₀ or ℓ^p, after a problem posed by Odell and Gowers.

Related

• Model Theory for C_p-theorists
• An Introduction To Continuous Model Theory
• Model theory of C^*-algebras
• On the undefinability of pathological Banach spaces
• Continuous logic in a classical setting