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arxiv: 2507.22181 · v2 · pith:37DBSLAMnew · submitted 2025-07-29 · 🧮 math.LO

Generic derivations on algebraically bounded structures II. Model theoretical properties

Fornasiero Antongiulio , Terzo Giuseppina This is my paper
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keywords algebraicallyboundeddeltaderivationsmodelpropertiesaboveattention
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Let T be an algebraically bounded theory. We consider the $L(\bar\delta)$-expansions of T by a tuple $\bar \delta$ of derivations (which may be commuting or not). We investigate the model completion of either of the above theories, whose existence has been established in [FT:24], with particular attention to its model-theoretic properties, including $\omega$-stability, simplicity, open core, and elimination of imaginaries.

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    Establishes minimality equivalences for geometric field theories and shows supersimplicity or superrosiness of generic derivation expansions holds precisely when the derivations commute, with rank bounds via Kolchin p...