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Preprint Number 2171

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2171. Alexander Berenstein, Christian d'Elbée, Evgueni Vassiliev
Vector spaces with a dense-codense generic submodule

Submission date: 22 April 2022


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.

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Full text arXiv 2204.10758: pdf, ps.

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