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Exponential-constructible functions in $P$-minimal structures

Logic 2018-02-26 v1 Number Theory

Abstract

Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers-Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under integration. In this paper we will present a natural refinement of their definition that allows for stability results to hold within the wider class of P-minimal structures. One of the main technical improvements is that we remove the requirement of definable Skolem functions from the proofs. As a result, we obtain stability in particular for all intermediate structures between the semi-algebraic and the sub-analytic languages.

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Cite

@article{arxiv.1802.08508,
  title  = {Exponential-constructible functions in $P$-minimal structures},
  author = {Saskia Chambille and Pablo Cubides Kovacsics and Eva Leenknegt},
  journal= {arXiv preprint arXiv:1802.08508},
  year   = {2018}
}

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24 pages