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Fractional parts of dense additive subgroups of real numbers

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Given a dense additive subgroup G of \(\mathbb {R}\) containing \(\mathbb {Z}\), we consider its intersection \(\mathbb {G}\) with the interval [0, 1[ with the induced order and the group structure given by addition modulo 1. We axiomatize the theory of \(\mathbb {G}\) and show it is model-complete, using a Feferman-Vaught type argument. We show that any sufficiently saturated model decomposes into a product of a standard part and two ordered semigroups of infinitely small and infinitely large elements.

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Authors and Affiliations

  1. Département de mathématiques, Université du Québec-UQAM, succ. Centre-ville, C.P. 8888, Montreal, QC, H3C 3P8, Canada

    Luc Bélair

  2. Département de Mathématique, Université de Mons, De Vinci, 20, Place du Parc, 7000, Mons, Belgium

    Françoise Point

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  1. Luc Bélair
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  2. Françoise Point
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Correspondence to Françoise Point.

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Presented by A. Dow.

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Luc Bélair was partially supported by NSERC and the second author by FRS-FNRS.

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Bélair, L., Point, F. Fractional parts of dense additive subgroups of real numbers. Algebra Univers. 79, 92 (2018). https://doi.org/10.1007/s00012-018-0572-2

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