Submission date: 7 July 2022

Abstract:

We consider an almost o-minimal expansion of an ordered group M=(M,<,+,0,...) and its tame extension N=(N,<,+,0,...). We demonstrate that the subset {x in M^n | N ⊧ Φ(x,a) } of M^n defined by a formula Φ(x,y) with M-bounded parameters a in N is M-definable. We also introduce its corollaries.

Mathematics Subject Classification: 03C64

Keywords and phrases:

Full text arXiv 2207.03021: pdf, ps.