Locally Polynomially Bounded Structures

Abstract

We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally definable in a fixed o-minimal and polynomially bounded reduct. As an application we show that in certain o-minimal structures definable functions are piecewise implicitly defined over the basic functions in the language.

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Cited by in corpus (8)

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• Local interdefinability of Weierstrass elliptic functions
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• Embedding the prime model of real exponentiation into o-minimal exponential fields
• Differential exponential topological fields
• Algebraic types in Zilber's exponential field
• Nondefinability results for elliptic and modular functions
• A nondefinability result for expansions of the ordered real field by the Weierstrass $\wp$ function