Lipschitz extensions of definable p‐adic functions

Mathematical Logic Quarterly 61 (3):151-158 (2015)
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Abstract

In this paper, we prove a definable version of Kirszbraun's theorem in a non‐Archimedean setting for definable families of functions in one variable. More precisely, we prove that every definable function, where and, that is λ‐Lipschitz in the first variable, extends to a definable function that is λ‐Lipschitz in the first variable.

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10.1002/malq.201400014

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References found in this work

On definable subsets of p-adic fields.Angus MacIntyre - 1976 - Journal of Symbolic Logic 41 (3):605-610.
A version of o-minimality for the p-adics.Deirdre Haskell & Dugald Macpherson - 1997 - Journal of Symbolic Logic 62 (4):1075-1092.
Algebraic theories with definable Skolem functions.Lou van den Dries - 1984 - Journal of Symbolic Logic 49 (2):625-629.
Algebraic Theories with Definable Skolem Functions.Lou van Den Dries - 1984 - Journal of Symbolic Logic 49 (2):625 - 629.
A Version Of $o$-minimality For The $p$-adics.Deirdre Haskell & Dugald Macpherson - 1997 - Journal of Symbolic Logic 62 (4):1075-1092.

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