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  1. Further Notes on Cell Decomposition in Closed Ordered Differential Fields.Cédric Rivière - 2009 - Annals of Pure and Applied Logic 159 (1-2):100-110.
    In [T. Brihaye, C. Michaux, C. Rivière, Cell decomposition and dimension function in the theory of closed ordered differential fields, Ann. Pure Appl. Logic .] the authors proved a cell decomposition theorem for the theory of closed ordered differential fields which generalizes the usual Cell Decomposition Theorem for o-minimal structures. As a consequence of this result, a well-behaving dimension function on definable sets in CODF was introduced. Here we continue the study of this cell decomposition in CODF by proving three (...)
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  • Definability of Types and VC Density in Differential Topological Fields.Françoise Point - 2018 - Archive for Mathematical Logic 57 (7-8):809-828.
    Given a model-complete theory of topological fields, we considered its generic differential expansions and under a certain hypothesis of largeness, we axiomatised the class of existentially closed ones. Here we show that a density result for definable types over definably closed subsets in such differential topological fields. Then we show two transfer results, one on the VC-density and the other one, on the combinatorial property NTP2.
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