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arXiv · 2409.11248

Neostability transfers in derivation-like theories

Omar Leon Sanchez·Shezad Mohamed
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Abstract

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.

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BibTeXRIS

Omar Leon Sanchez, Shezad Mohamed. 2024-09-17. Neostability transfers in derivation-like theories. https://arxiv.org/abs/2409.11248

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