Externally definable quotients and NIP expansions of the real ordered additive group [article]

Erik Walsberg
2020 arXiv   pre-print
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
more » ... endent if and only if R is either o-minimal or (R,<,+,αZ)-minimal for some α > 0.
arXiv:1910.10572v3 fatcat:i6ui3zglxvalhh3l4dpvgktdqi