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arXiv · 2211.14628

Invariant Keisler measures for omega-categorical structures

Paolo Marimon
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Abstract

A recent article of Chernikov, Hrushovski, Kruckman, Krupinski, Moconja, Pillay and Ramsey finds the first examples of simple structures with formulas which do not fork over $\emptyset$ but are universally measure zero. In this article we give the first known simple $\omega$-categorical counterexamples. These happen to be various $\omega$-categorical Hrushovski constructions. Using a probabilistic independence theorem from Jahel and Tsankov, we show how simple $\omega$-categorical structures where the forking ideal and the universally measure zero ideal coincide must satisfy a stronger version of the independence theorem.

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Paolo Marimon. 2022-11-26. Invariant Keisler measures for omega-categorical structures. https://doi.org/10.1017/jsl.2024.39

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