Submission date: 10 December 2018

Abstract:

We show that, for a certain large class of power-bounded o-minimal L_T-theories T whose field of exponents is infinite-dimensional as a vector space over the rationals, any definable set in a T-convex valued field (R, O) is in a precise sense the limit of a family of L_T-definable sets indexed over the residue field. Alternatively, in the mainstream model-theoretic language, this says that if (R', O') is an elementary substructure of (R, O) and if the residue field of O contains an element that is infinitesimal relative to the residue field of O' then any set A ⊆ (R')^m definable in (R', O') is the trace of a set definable in R.

Mathematics Subject Classification: 03C64, 12J10

Keywords and phrases:

Full text arXiv 1812.03590: pdf, ps.