Derivation-like theories and neostability |
Shezad Mohamed (University of Manchester) |
Dienstag, 28. Januar 2025 14:30Uhr |
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Motivated by structural properties of differential field extensions, Omar Leon Sanchez and I introduced the notion of a theory T being derivation-like with respect to another model complete theory $T_0$. We proved that when T admits a model companion $T^+$, then several model-theoretic properties are transferred from $T_0$ to $T^+$. These properties include completeness, quantifier elimination, stability, simplicity, and NSOP$_1$. Examples of derivation-like theories are plentiful but are typically obtained by adding extra structure to theories of fields. In this talk I will introduce the central notions, detail how the proofs work by lifting independence relations from $T_0$ to $T^+$, and give examples. |