Model Theory for C_p-theorists

2020/04/14 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) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2004.06537

openalex publication_date 2020/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey discrete and continuous model-theoretic notions which have important connections to general topology. We present a self-contained exposition of several interactions between continuous logic and C_p-theory which have applications to a classification problem involving Banach spaces not including c₀ or l^p, following recent results obtained by P. Casazza and J. Iovino for compact continuous logics. Using C_p-theoretic results involving Grothendieck spaces and double limit conditions, we extend their results to a broader family of logics, namely those with a first countable weakly Grothendieck space of types. We pose C_p-theoretic problems which have model-theoretic implications.

Citations

• Correspondences between model theory and Banach space theory

Related

• C_p-Theory for Model Theorists
• Continuous logic in a classical setting
• On the undefinability of pathological Banach spaces
• An Introduction To Continuous Model Theory
• Elements of affine model theory