2018/02/23 by Saskia Chambille, Chambille, Saskia, Pablo Cubides Kovacsics +3
Mathematics · #03C52 #11S80 #11U09 #12J12 #12J25 #28A25 #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT) #math.LO #math.NT #msc:03C52 #msc:11S80 #msc:11U09 #msc:12J12 #msc:12J25 #msc:28A25
paper · pdf · doi:10.48550/arxiv.1802.08508
24 pages
arxiv created 2018/02/23 · arxiv updated 2018/02/26
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.