Cell decompositions of C-minimal structures

Annals of Pure and Applied Logic 66 (2):113-162 (1994)

Abstract
C-minimality is a variant of o-minimality in which structures carry, instead of a linear ordering, a ternary relation interpretable in a natural way on set of maximal chains of a tree. This notion is discussed, a cell-decomposition theorem for C-minimal structures is proved, and a notion of dimension is introduced. It is shown that C-minimal fields are precisely valued algebraically closed fields. It is also shown that, if certain specific ‘bad’ functions are not definable, then algebraic closure has the exchange property, and for definable sets dimension coincides with the rank obtained from algebraic closure
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DOI 10.1016/0168-0072(94)90064-7
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References found in this work BETA

On Variants of o-Minimality.Dugald Macpherson & Charles Steinhorn - 1996 - Annals of Pure and Applied Logic 79 (2):165-209.
More on Definable Sets of P-Adic Numbers.Philip Scowcroft - 1988 - Journal of Symbolic Logic 53 (3):912-920.

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Citations of this work BETA

On Variants of o-Minimality.Dugald Macpherson & Charles Steinhorn - 1996 - Annals of Pure and Applied Logic 79 (2):165-209.
A Version of o-Minimality for the P-Adics.Deirdre Haskell & Dugald Macpherson - 1997 - Journal of Symbolic Logic 62 (4):1075-1092.
B-Minimality.Raf Cluckers & François Loeser - 2007 - Journal of Mathematical Logic 7 (2):195-227.

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