Submission date: 22 April 2022

Abstract:

We study expansions of a vector space V over a field F, possibly with extra structure, with a generic submodule over a subring of 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 expansions preserve tame model theoretic properties such as stability, NIP, NTP_1, NTP_2 and NSOP_1. We also study induced independence relations in the expansion.

Mathematics Subject Classification:

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Full text arXiv 2204.10758: pdf, ps.