Cell decomposition and definable functions for weak p‐adic structures

Mathematical Logic Quarterly 58 (6):482-497 (2012)
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Abstract

We develop a notion of cell decomposition suitable for studying weak p‐adic structures (reducts of p‐adic fields where addition and multiplication are not (everywhere) definable). As an example, we consider a structure with restricted addition.

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10.1002/malq.201200031

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Citations of this work

Reducts of p-adically closed fields.Eva Leenknegt - 2014 - Archive for Mathematical Logic 53 (3-4):285-306.
Cell decomposition for semibounded p-adic sets.Eva Leenknegt - 2013 - Archive for Mathematical Logic 52 (5-6):667-688.

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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.
Cell decomposition for P‐minimal fields.Marie-Hélène Mourgues - 2009 - Mathematical Logic Quarterly 55 (5):487-492.
A structure theorem for semibounded sets in the reals.Ya'acov Peterzil - 1992 - Journal of Symbolic Logic 57 (3):779-794.
A version of p-adic minimality.Raf Cluckers & Eva Leenknegt - 2012 - Journal of Symbolic Logic 77 (2):621-630.

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