an:05563895
Zbl 1166.03015
Brihaye, Thomas; Michaux, Christian; Rivi??re, C??dric
Cell decomposition and dimension function in the theory of closed ordered differential fields
EN
Ann. Pure Appl. Logic 159, No. 1-2, 111-128 (2009).
00250042
2009
j
03C64 12H05 12J15 12L12
ordered differential fields; cell decomposition; dimension function
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.