Vector spaces with a dense-codense generic submodule

Abstract

We study expansions of a vector space $V$ over a field $\mathbb{F}$, possibly with extra structure, with a generic submodule over a subring of $\mathbb{F}$. We construct a natural expansion by existentially defined functions so that the expansion in the extended language satisfies quantifier elimination. We show that this expansion preserves tame model theoretic properties such as stability, NIP, NTP${}_1$, NTP${}_2$ and NSOP${}_1$. We also study induced independence relations in the expansion.

41 pages

Cited by in corpus (1)

• Preservation of NATP