Neostability transfers in derivation-like theories
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912288164806656 |
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| author | Sanchez, Omar Leon Mohamed, Shezad |
| author_facet | Sanchez, Omar Leon Mohamed, Shezad |
| contents | Motivated by structural properties of differential field extensions, we introduce the notion of a theory $T$ being derivation-like with respect to another model complete theory $T_0$. We prove that when $T$ admits a model companion $T_+$, several model-theoretic properties transfer from $T_0$ to $T_+$. These properties include completeness, quantifier elimination, stability, simplicity, and NSOP$_1$. We also observe that, aside from the theory of differential fields, examples of derivation-like theories are plentiful. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neostability transfers in derivation-like theories Sanchez, Omar Leon Mohamed, Shezad Logic 03C45, 03C60, 12H05 Motivated by structural properties of differential field extensions, we introduce the notion of a theory $T$ being derivation-like with respect to another model complete theory $T_0$. We prove that when $T$ admits a model companion $T_+$, several model-theoretic properties transfer from $T_0$ to $T_+$. These properties include completeness, quantifier elimination, stability, simplicity, and NSOP$_1$. We also observe that, aside from the theory of differential fields, examples of derivation-like theories are plentiful. |
| title | Neostability transfers in derivation-like theories |
| topic | Logic 03C45, 03C60, 12H05 |
| url | https://arxiv.org/abs/2409.11248 |