Cell decomposition and dimension function in the theory of closed ordered differential fields

Annals of Pure and Applied Logic 159 (1-2):111-128 (2009)
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Abstract

In this paper we develop a differential analogue of o-minimal cell decomposition for the theory CODF of closed ordered differential fields. Thanks to this differential cell decomposition we define a well-behaving dimension function on the class of definable sets in CODF. We conclude this paper by proving that this dimension is closely related to both the usual differential transcendence degree and the topological dimension associated, in this case, with a natural differential topology on ordered differential fields

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Christian Michaux
University of Mons

References found in this work

The model theory of ordered differential fields.Michael F. Singer - 1978 - Journal of Symbolic Logic 43 (1):82-91.
Further notes on cell decomposition in closed ordered differential fields.Cédric Rivière - 2009 - Annals of Pure and Applied Logic 159 (1-2):100-110.

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