Extreme types and extremal models

2024/01/15 by Bagheri, Seyed-Mohammad · 2 citations
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2401.07804

Abstract

In the affine fragment of continuous logic, type spaces are compact convex sets. I study some model theoretic properties of extreme types. It is proved that every complete theory T has an extremal model, i.e. a model which realizes only extreme types. Extremal models form an elementary class in the full continuous logic sense if and only if the set of extreme n-types is closed in S_n(T) for each n. Also, some applications are given in the special cases where the theory has a compact or first order model.

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