Definably amenable groups in Continuous logic
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913770681401344 |
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| author | Carmona, Juan Felipe Onshuus, Alf |
| author_facet | Carmona, Juan Felipe Onshuus, Alf |
| contents | We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both notions using fixed-point properties. We show that stable and ultracompact groups are definably amenable and prove that, for groups definable in dependent theories, definable amenability is equivalent to the existence of an f-generic type. Finally, we show the randomizations of first-order definably amenable groups are extremely definably amenable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_09971 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Definably amenable groups in Continuous logic Carmona, Juan Felipe Onshuus, Alf Logic 03C66 03C45 43A07 We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both notions using fixed-point properties. We show that stable and ultracompact groups are definably amenable and prove that, for groups definable in dependent theories, definable amenability is equivalent to the existence of an f-generic type. Finally, we show the randomizations of first-order definably amenable groups are extremely definably amenable. |
| title | Definably amenable groups in Continuous logic |
| topic | Logic 03C66 03C45 43A07 |
| url | https://arxiv.org/abs/2201.09971 |