Abstract
We introduce the notion of R-analytic functions. These are definable in an o-minimal expansion of a real closed field R and are locally the restriction of a K-differentiable function (defined by Peterzil and Starchenko) where \(K=R[\sqrt{-1}]\) is the algebraic closure of R. The class of these functions in this general setting exhibits the nice properties of real analytic functions. We also define strongly R-analytic functions. These are globally the restriction of a K-differentiable function. We show that in arbitrary models of important o-minimal theories strongly R-analytic functions abound and that the concept of analytic cell decomposition can be transferred to non-standard models.
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The author was supported in part by DFG KA 3297/1-2.
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Kaiser, T. R-analytic functions. Arch. Math. Logic 55, 605–623 (2016). https://doi.org/10.1007/s00153-016-0483-x
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DOI: https://doi.org/10.1007/s00153-016-0483-x
Keywords
- R-analytic functions
- Weierstraß preparation and division
- o-Minimal theories with global complexification