Neostability transfers in derivation-like theories
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 $T_+$, then several model-theoretic properties transfer from $T_0$ t...
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| creator | Sanchez, Omar Leon Mohamed, Shezad |
| description | 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 $T_+$, then 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. |
| doi_str_mv | 10.48550/arxiv.2409.11248 |
| format | Article |
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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 $T_+$, then 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
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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 $T_+$, then 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
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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 $T_+$, then 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.</abstract><doi>10.48550/arxiv.2409.11248</doi><oa>free_for_read</oa></addata></record> |
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| title | Neostability transfers in derivation-like theories |
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