Submission date: 26 November 2022

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 ∅ but are universally measure zero. In this article we give the first known simple ω-categorical counterexamples. These happen to be various ω-categorical Hrushovski constructions. Using a probabilistic independence theorem from Jahel and Tsankov, we show how simple ω-categorical structures where the forking ideal and the universally measure zero ideal coincide must satisfy a stronger version of the independence theorem.

Mathematics Subject Classification: 03C68

Keywords and phrases:

Full text arXiv 2211.14628: pdf, ps.