Externally definable fsg groups in NIP theories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912456353251328 |
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| author | Chernikov, Artem |
| author_facet | Chernikov, Artem |
| contents | We show that every fsg group externally definable in an NIP structure is definably isomorphic to a group interpretable in it. Our proof relies on honest definitions and a group chunk result reconstructing a hyper-definable group from its multiplication given generically with respect to a translation invariant definable Keisler measure on it. We obtain related results on externally (type-)definable sets and groups, including a proof of a conjecture of Eleftheriou on fsg groups in real closed valued fields, and a description of externally definable, definably amenable subgroups of definable groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_23265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Externally definable fsg groups in NIP theories Chernikov, Artem Logic Group Theory 03C45, 03C60, 03C64, 28D15 We show that every fsg group externally definable in an NIP structure is definably isomorphic to a group interpretable in it. Our proof relies on honest definitions and a group chunk result reconstructing a hyper-definable group from its multiplication given generically with respect to a translation invariant definable Keisler measure on it. We obtain related results on externally (type-)definable sets and groups, including a proof of a conjecture of Eleftheriou on fsg groups in real closed valued fields, and a description of externally definable, definably amenable subgroups of definable groups. |
| title | Externally definable fsg groups in NIP theories |
| topic | Logic Group Theory 03C45, 03C60, 03C64, 28D15 |
| url | https://arxiv.org/abs/2506.23265 |