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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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| _version_ | 1866909749809774592 |
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| author | Marimon, Paolo |
| author_facet | Marimon, Paolo |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_14628 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Invariant Keisler measures for omega-categorical structures Marimon, Paolo Logic 03C68 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. |
| title | Invariant Keisler measures for omega-categorical structures |
| topic | Logic 03C68 |
| url | https://arxiv.org/abs/2211.14628 |