O-minimal analytic separation of sets in dimension 2

Annals of Pure and Applied Logic 157 (2-3):130-138 (2009)
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Abstract

We study the Hardy field associated with an o-minimal expansion of the real numbers. If the set of analytic germs is dense in the Hardy field, then we can definably analytically separate sets in , and we can definably analytically approximate definable continuous unary functions. A similar statement holds for definable smooth functions

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10.1016/j.apal.2008.09.005

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References found in this work

Expansions of the real field with power functions.Chris Miller - 1994 - Annals of Pure and Applied Logic 68 (1):79-94.
O -minimal Λ m -regular stratification.Andreas Fischer - 2007 - Annals of Pure and Applied Logic 147 (1):101-112.
On defining c∞.A. J. Wilkie - 1994 - Journal of Symbolic Logic 59 (1):344 -.

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