A model theoretic Baire category theorem for simple theories

2009/12/14 by Ziv Shami, Shami, Ziv
Computer Science · Mathematics · #03C45 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.0912.2591

openalex publication_date 2009/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a model theoretic Baire category theorem for τ_low^f-sets in a countable simple theory in which the extension property is first-order and show some of its applications. We also prove a trichotomy for minimal types in countable nfcp theories: either every type that is internal in a minimal type is essentially-1-based by means of the forking topology or T interprets an infinite definable 1-based group of finite D-rank or T interprets a strongly-minimal formula.

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