Definable quotients in d-minimal structures

Abstract

We consider d-minimal expansions of ordered fields. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several technical conditions are satisfied. These conditions are satisfied when there is a definable proper action of a definable group $G$ on a locally closed definable subset $X$ of $F^n$, where $F$ is the universe.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2212.06401