Models of an abstract elementary class as a Generalized Polish Space
Abstract
Abstract In first order logic, it is known that you can define a topology so that the countable models of some theory $T$ form a Polish Space. In this paper we use the Baldwin–Boney Relational Presentation Theorem (from [3]) to generalize this result to the models of an Abstract Elementary Class (AEC). More specifically, we define a topology on the models of an AEC of size $\lambda \geq \kappa $, where $\kappa $ is the L$\ddot{o}$wenheim–Skolem number and $\lambda $ has to satisfy a set-theoretic assumption and prove that these models form a Generalized Polish Space.
Fields of Study & Subjects
Advanced Topology and Set Theory
Advanced Algebra and Logic
Advanced Banach Space Theory
Publication details
- Journal / source
- Logic Journal of IGPL
- Volume
- 34
- Issue
- 3
- Publication date
- 22 January 2026
- Language
- EN