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Cell decomposition for P‐minimal fields
Mathematical Logic Quarterly 55 (5):487-492 (2009)
Abstract
In [12], 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 in [6]. We prove that a P-minimal field K admits cell decomposition if and only if K has definable selection. A preprint version in French of this result appeared as a prepublication [8]Links
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Citations of this work
Topological cell decomposition and dimension theory in p-minimal fields.Pablo Cubides Kovacsics, Luck Darnière & Eva Leenknegt - 2017 - Journal of Symbolic Logic 82 (1):347-358.
A version of p-adic minimality.Raf Cluckers & Eva Leenknegt - 2012 - Journal of Symbolic Logic 77 (2):621-630.
Cell decomposition and classification of definable sets in p-optimal fields.Luck Darnière & Immanuel Halpuczok - 2017 - Journal of Symbolic Logic 82 (1):120-136.
A p-minimal structure without definable Skolem functions.Pablo Cubides Kovacsics & Kien Huu Nguyen - 2017 - Journal of Symbolic Logic 82 (2):778-786.
Clustered cell decomposition in P-minimal structures.Saskia Chambille, Pablo Cubides Kovacsics & Eva Leenknegt - 2017 - Annals of Pure and Applied Logic 168 (11):2050-2086.
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.
On the structure of semialgebraic sets over p-adic fields.Philip Scowcroft & Lou van den Dries - 1988 - Journal of Symbolic Logic 53 (4):1138-1164.
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