2025/03/28 by Marangelis, Georgios
#03E15 #54E52 #54H05 #FOS: Mathematics #Logic (math.LO) #Primary 03C48 #Secondary 03C75
paper · doi:10.48550/arxiv.2503.22287
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 (i.e. completely metrizable second countable space). In this paper we use the Baldwin- Boney Relational Presentation Theorem (from [3]; cf. 2.3) 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 λ≥ κ, where κ is the Lowenheim-Skolem number and λ has to satisfy a set-theoretic assumption (see Section 4) and prove that these models form a Generalized Polish Space (i.e. a generalization of Polish Spaces i.e. completely G-metrizable space with weight ≤ κ).