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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2407.12452 |
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| _version_ | 1866911060837007360 |
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| author | d'Elbée, Christian Müller, Isabel Ramsey, Nicholas Siniora, Daoud |
| author_facet | d'Elbée, Christian Müller, Isabel Ramsey, Nicholas Siniora, Daoud |
| contents | We prove the existence of a model companion of the two-sorted theory of $c$-nilpotent Lie algebras over a field satisfying a given theory of fields. We describe a language in which it admits relative quantifier elimination up to the field sort. Using a new criterion which does not rely on a stationary independence relation, we prove that if the field is NSOP$_1$, then the model companion is NSOP$_4$. We also prove that if the field is algebraically closed, then the model companion is $c$-NIP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12452 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A two-sorted theory of nilpotent Lie algebras d'Elbée, Christian Müller, Isabel Ramsey, Nicholas Siniora, Daoud Logic We prove the existence of a model companion of the two-sorted theory of $c$-nilpotent Lie algebras over a field satisfying a given theory of fields. We describe a language in which it admits relative quantifier elimination up to the field sort. Using a new criterion which does not rely on a stationary independence relation, we prove that if the field is NSOP$_1$, then the model companion is NSOP$_4$. We also prove that if the field is algebraically closed, then the model companion is $c$-NIP. |
| title | A two-sorted theory of nilpotent Lie algebras |
| topic | Logic |
| url | https://arxiv.org/abs/2407.12452 |