Submission date: 10 November 2008

Abstract:

P. Scowcroft and L. van den Dries proved a Cell Decomposition Theorem for p-adically closed fields. We work here with the notion of P-minimal fields defined by D. Haskell and D. Macpherson. We prove that a P-minimal field K admits cell decomposition if and only if K has definable selection.

Mathematics Subject Classification: 03C60; 03C98; 12L12; 12J10

Keywords and phrases: Cell decomposition, p-minimality, p-adic number, Henselian valued field

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