Generic derivations on algebraically bounded structures II Model theoretical properties

TL;DR

This paper studies the model-theoretic properties of algebraically bounded theories expanded by derivations, focusing on their model completion and properties like stability, simplicity, and elimination of imaginaries.

Contribution

It analyzes the model-theoretic characteristics of the model completion of derivation-extended algebraically bounded theories, building on prior existence results.

Findings

Establishes conditions for $ ext{ω}$-stability and simplicity.

Examines open core and elimination of imaginaries in the expanded theories.

Provides insights into the model-theoretic behavior of derivation expansions.

Abstract

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.