On groups and fields interpretable in $\mathrm{NTP_2}$ fields
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910772814151680 |
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| author | Wang, Paul Z. |
| author_facet | Wang, Paul Z. |
| contents | This paper aims at developing model-theoretic tools to study interpretable fields and definably amenable groups, mainly in $\mathrm{NIP}$ or $\mathrm{NTP_2}$ settings. An abstract theorem constructing definable group homomorphisms from generic data is proved. It relies heavily on a stabilizer theorem of Montenegro, Onshuus and Simon. The main application is a structure theorem for definably amenable groups that are interpretable in algebraically bounded perfect $\mathrm{NTP_2}$ fields with bounded Galois group (under some mild assumption on the imaginaries involved), or in algebraically bounded theories of (differential) NIP fields. These imply a classification of the fields interpretable in differentially closed valued fields, and structure theorems for fields interpretable in finitely ramified henselian valued fields of characteristic $0$, or in NIP algebraically bounded differential fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09143 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On groups and fields interpretable in $\mathrm{NTP_2}$ fields Wang, Paul Z. Logic 03C45 This paper aims at developing model-theoretic tools to study interpretable fields and definably amenable groups, mainly in $\mathrm{NIP}$ or $\mathrm{NTP_2}$ settings. An abstract theorem constructing definable group homomorphisms from generic data is proved. It relies heavily on a stabilizer theorem of Montenegro, Onshuus and Simon. The main application is a structure theorem for definably amenable groups that are interpretable in algebraically bounded perfect $\mathrm{NTP_2}$ fields with bounded Galois group (under some mild assumption on the imaginaries involved), or in algebraically bounded theories of (differential) NIP fields. These imply a classification of the fields interpretable in differentially closed valued fields, and structure theorems for fields interpretable in finitely ramified henselian valued fields of characteristic $0$, or in NIP algebraically bounded differential fields. |
| title | On groups and fields interpretable in $\mathrm{NTP_2}$ fields |
| topic | Logic 03C45 |
| url | https://arxiv.org/abs/2402.09143 |