A model theoretic Baire category theorem for simple theories
Ziv Shami

TL;DR
This paper establishes a model theoretic Baire category theorem for certain sets in countable simple theories with the extension property, and applies it to classify minimal types in nfcp theories.
Contribution
It introduces a new Baire category theorem for $ ilde\tau_{low}^f$-sets and proves a trichotomy for minimal types in countable nfcp theories.
Findings
A Baire category theorem for $ ilde\tau_{low}^f$-sets in simple theories
A trichotomy classification for minimal types in nfcp theories
Identification of conditions for interpretability of groups or minimal formulas
Abstract
We prove a model theoretic Baire category theorem for -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 interprets an infinite definable 1-based group of finite -rank or interprets a strongly-minimal formula.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms
