2023/04/20 by Samaria Montenegro, Montenegro, Samaria, Silvain Rideau-Kikuchi +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.2304.10433
openalex publication_date 2023/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Pseudo algebraically closed, pseudo real closed, and pseudo p-adically closed fields are examples of unstable fields that share many similarities, but have mostly been studied separately. In this text, we propose a unified framework for studying them: the class of pseudo T-closed fields, where T is an enriched theory of fields. These fields verify a "local-global" principle for the existence of points on varieties with respect to models of T. This approach also enables a good description of some fields equipped with multiple V-topologies, particularly pseudo algebraically closed fields with a finite number of valuations. One important result is a (model theoretic) classification result for bounded pseudo T-closed fields, in particular we show that under specific hypotheses on T, these fields are NTP2 of finite burden.