Francis Oger

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In the present paper, as we did previously in [5], we investigate the relations between the geometric properties of tilings and the algebraic and model-theoretic properties of associated relational structures. Our study is motivated by the existence of aperiodic tilings. In [5], we considered tilings of the euclidean spaces R, and isomorphism was defined up(More)
If M and Nare ordered groups, we denote by Mx N the group MxNequipped with the lexicographical order: (a,b) < (a',b') if and only if a < a' or {a = a' and b < b'). In [1], A. L. S. Corner gives an example of two countable abelian groups A, G such that G and A x A x G are isomorphic while G and A x G are not isomorphic; he also gives an example of two(More)
In this paper, we show that any finitely generated abelian-byfinite group is an elementary submodel of its profinite completion. It follows that two finitely generated abelian-by-finite groups are elementarily equivalent if and only if they have the same finite images. We give an example of two finitely generated abelian-by-finite groups G, H which satisfy(More)
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