Noetherian theories
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866911984950181888 |
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| author | Martin-Pizarro, Amador Ziegler, Martin |
| author_facet | Martin-Pizarro, Amador Ziegler, Martin |
| contents | A first-order theory is Noetherian with respect to the collection of formulae $\mathcal{F}$ if every definable set is a Boolean combination of instances of formulae in $\mathcal{F}$ and the topology whose subbasis of closed sets is the collection of instances of arbitrary formulae in $\mathcal{F}$ is Noetherian. Noetherianity is a strengthening of equationality, which itself implies stability. We show the Noetherianity of the theory of proper pairs of algebraically closed fields in any characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16826 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Noetherian theories Martin-Pizarro, Amador Ziegler, Martin Logic 03C45, 12H05 A first-order theory is Noetherian with respect to the collection of formulae $\mathcal{F}$ if every definable set is a Boolean combination of instances of formulae in $\mathcal{F}$ and the topology whose subbasis of closed sets is the collection of instances of arbitrary formulae in $\mathcal{F}$ is Noetherian. Noetherianity is a strengthening of equationality, which itself implies stability. We show the Noetherianity of the theory of proper pairs of algebraically closed fields in any characteristic. |
| title | Noetherian theories |
| topic | Logic 03C45, 12H05 |
| url | https://arxiv.org/abs/2307.16826 |