Submission date: 28 January 2021

Abstract:

We introduce trace definability, a weak notion of interpretability, and trace equivalence, a weak notion of equivalence for first order structures and theories. In particular we get an interesting weak equivalence notion for \mathrm{NIP} theories. We describe a close connection to indiscernible collapse. We also show that if Q is a divisible subgroup of (ℝ;+) and Q is a dp-rank one expansion of (Q;+,<) then exactly one of the following holds: Th(Q) trace defines RCF or Q is trace equivalent to a reduct of an ordered vector space.

Mathematics Subject Classification:

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Full text arXiv 2101.12194: pdf, ps.