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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.14628 |
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Table of Contents:
- 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 $ω$-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.