Eberlein-Smulian compactness and Kolmogorov extension theorems; a model theoretic approach

TL;DR

This paper extends the Kolmogorov extension theorem to unbounded variables using integral logic and provides a model-theoretic proof of the Eberlein-Smulian compactness theorem, highlighting connections to classification theory.

Contribution

It introduces a model-theoretic approach to classical compactness theorems, extending their applicability and revealing new theoretical links.

Findings

Extended Kolmogorov extension theorem to unbounded variables

Provided a model-theoretic proof of Eberlein-Smulian compactness

Established connections between compactness theorems and classification theory

Abstract

This paper has two parts. First, we complete the proof of the Kolmogorov extension theorem for unbounded random variables using compactness theorem of integral logic which was proved for bounded case in [8]. Second, we give a proof of the Eberlein-Smulian compactness theorem by Ramsey's theorem and point out the correspondence between this theorem and a result in Shelah's classification theory.