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Cell decomposition and dimension function in the theory of closed ordered differential fields. (English) Zbl 1166.03015
Summary: 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 (called \(\delta \)-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.

MSC:
03C64 Model theory of ordered structures; o-minimality
12H05 Differential algebra
12J15 Ordered fields
12L12 Model theory of fields
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