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Externally definable quotients and NIP expansions of the real ordered additive group
[article]
2020
arXiv
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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
arXiv:1910.10572v3
fatcat:i6ui3zglxvalhh3l4dpvgktdqi