Locally Polynomially Bounded Structures

Details Locally Polynomially Bounded Structures Locally Polynomially Bounded Structures

2007-01-18

arxiv.org/abs/math/0701523v2

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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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