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- Francis Oger
- Theor. Comput. Sci.
- 2004

- Francis Oger
- J. Symb. Log.
- 2001

- Francis Oger
- 2010

For each integer n, an n-folding curve is obtained by folding n times a strip of paper in two, possibly up or down, and unfolding it with right angles. Generalizing the usual notion of infinite folding curve, we define complete folding curves as the curves without endpoint which are unions of increasing sequences of n-folding curves for n integer. We prove… (More)

- Francis Oger
- 2009

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)

- Francis Oger
- J. Symb. Log.
- 1984

The aim of this paper is to describe (without proofs) an analogue of the theory of nontrivial torsion-free divisible abelian groups for metabelian groups. We obtain illustrations for “old-fashioned” model theoretic algebra and “new” examples in the theory of stable groups. We begin this paper with general considerations about model theory. In the second… (More)

- Francis Oger
- Arch. Math. Log.
- 2001

- Francis Oger
- 1987

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)

- Francis Oger, Thomas Jech
- 2010

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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