Differentiation in P-minimal structures and a p-adic Local Monotonicity Theorem
Logic
2014-04-17 v2
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.
Cite
@article{arxiv.1303.6429,
title = {Differentiation in P-minimal structures and a p-adic Local Monotonicity Theorem},
author = {Tristan Kuijpers and Eva Leenknegt},
journal= {arXiv preprint arXiv:1303.6429},
year = {2014}
}
Comments
17 pages