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arXiv · 1802.08508

Exponential-constructible functions in $P$-minimal structures

Saskia Chambille·Pablo Cubides Kovacsics·Eva Leenknegt
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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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Saskia Chambille, Pablo Cubides Kovacsics, Eva Leenknegt. 2018-02-23. Exponential-constructible functions in $P$-minimal structures. https://arxiv.org/abs/1802.08508

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