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DIFFERENTIATION IN P-MINIMAL STRUCTURES AND A p-ADIC LOCAL MONOTONICITY THEOREM

Published online by Cambridge University Press:  12 December 2014

TRISTAN KUIJPERS  and
EVA LEENKNEGT
TRISTAN KUIJPERS
Affiliation:
KU LEUVEN DEPARTMENT OF MATHEMATICS CELESTIJNENLAAN 200B 3001 LEUVEN, BELGIUME-mail: tristan.kuijpers@wis.kuleuven.be
EVA LEENKNEGT
Affiliation:
PURDUE UNIVERSITY DEPARTMENT OF MATHEMATICS 150 N. UNIVERSITY STREET WEST LAFAYETTE, IN 47907-2067, USAE-mail: eleenkne@math.purdue.edu
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Abstract

We prove a p-adic, local version of the Monotonicity Theorem for P-minimal structures. The existence of such a theorem was originally conjectured by Haskell and Macpherson. We approach the problem by considering the first order strict derivative. In particular, we show that, for a wide class of P-minimal structures, the definable functions f : K → K are almost everywhere strictly differentiable and satisfy the Local Jacobian Property.

Keywords

P-minimalityp-adic differentiationmonotonicity
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 4 , December 2014 , pp. 1133 - 1147
Copyright
Copyright © The Association for Symbolic Logic 2014 

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