2022/11/26 by Paolo Marimon, Marimon, Paolo
Mathematics · Computer Science · #Advanced Topology and Set Theory #Advanced Algebra and Logic #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2211.14628
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.