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Preprint Number 1146

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1146. Chris Miller and Athipat Thamrongthanyalak
D-minimal expansions of the real field have the C^p zero set property

Submission date: 19 January 2017


Let E be a closed subset of R^n and p be a natural number. If the structure (R,+,×,E) is d-minimal (that is, in every structure elementarily equivalent to (R,+,×,E), every unary definable set is a disjoint union of open intervals and finitely many discrete sets), then there exist C^p functions f: R^n → R definable in (R,+,×,E) such that E is the zero set of f.

Mathematics Subject Classification: Primary 26B05; Secondary 03C64

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