MODNET
Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1665

Preprint Number 1665

Previous Next Preprint server


1665. Erik Walsberg
Externally definable quotients and NIP expansions of the real ordered additive group
E-mail:

Submission date: 23 October 2019

Abstract:

Let R be an NIP expansion of (ℝ, < , + ) by closed subsets of ℝ^n and continuous functions f : ℝ^m → ℝ^n. Then R is generically locally o-minimal. It follows that if X ⊆ ℝ^n is definable in R then the C^k-points of X are dense in X for any k ≥ 0. This follows from a more general theorem on NIP expansions of locally compact groups, which itself follows from a result on quotients of definable sets by equivalence relations which are externally definable and ⋀-definable. We also show that R is strongly dependent if and only if R is either o-minimal or interdefinable with (ℝ, < , + , B, αℤ) for some α > 0 and collection B of bounded subsets of ℝ^n such that (ℝ, < , + , B) is o-minimal.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1910.10572: pdf, ps.


Last updated: October 25 2019 14:09 Please send your corrections to: