See also
  1.  3
    Presburger Arithmetic and Recognizability of Sets of Natural Numbers by Automata: New Proofs of Cobham's and Semenov's Theorems.Christian Michaux & Roger Villemaire - 1996 - Annals of Pure and Applied Logic 77 (3):251-277.
    Let be the set of nonnegative integers. We show the two following facts about Presburger's arithmetic:1. 1. Let . If L is not definable in , + then there is an definable in , such that there is no bound on the distance between two consecutive elements of L′. and2. 2. is definable in , + if and only if every subset of which is definable in is definable in , +. These two Theorems are of independent interest but we (...)
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    Cell Decomposition and Dimension Function in the Theory of Closed Ordered Differential Fields.Thomas Brihaye, Christian Michaux & Cédric Rivière - 2009 - Annals of Pure and Applied Logic 159 (1-2):111-128.
    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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    Preface.Catherine Finet & Christian Michaux - 2001 - Annals of Pure and Applied Logic 111 (1-2):1-2.