2017/10/16 by Christopher J. Eagle, Eagle, Christopher J., Franklin D. Tall +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.1710.05889
openalex publication_date 2017/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Omitting Types Theorem in model theory and the Baire Category Theorem in topology are known to be closely linked. We examine the precise relation between these two theorems. Working with a general notion of logic we show that the classical Omitting Types Theorem holds for a logic if a certain associated topological space has all closed subspaces Baire. We also consider stronger Baire category conditions, and hence stronger Omitting Types Theorems, including a game version. We use examples of spaces previously studied in set-theoretic topology to produce abstract logics showing that the game Omitting Types statement is consistently not equivalent to the classical one.