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Preprint Number 570
570. Tristan Kuijpers and Eva Leenknegt
Differentiation in P-minimal structures and a p-adic Local Monotonicity Theorem
Submission date: 26 March 2013.
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.
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