5 found
  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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    Completely Decomposable Abelian Groups -Categorical Over a Subgroup.Roger Villemaire - 1992 - Archive for Mathematical Logic 31 (4):263-275.
  3.  17
    Theories of Modules Closed Under Direct Products.Roger Villemaire - 1992 - Journal of Symbolic Logic 57 (2):515-521.
    We generalize to theories of modules (complete or not) a result of U. Felgner stating that a complete theory of abelian groups is a Horn theory if and only if it is closed under products. To prove this we show that a reduced product of modules $\Pi_F M_i (i \in I)$ is elementarily equivalent to a direct product of ultraproducts of the modules $M_i (i \in I)$.
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    Homogeneity and Fix-Points: Going Forth!Roger Villemaire - 2015 - Journal of Symbolic Logic 80 (2):636-660.
  5.  4
    Reasoning About Visibility.Roger Villemaire & Sylvain Hallé - 2012 - Journal of Applied Logic 10 (2):163-178.