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Preprint Number 1259

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1259. Luc Bélair and Françoise Point
Fractional Parts of Dense Additive Subgroups of Real Numbers

Submission date: 19 July 2017


Given a dense additive subgroup G of R containing Z, we consider its intersection G with the interval [0,1[ with the induced order and the group structure given by addition modulo 1. We axiomatize the theory of 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.

Mathematics Subject Classification: 03C60, 06F05

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Full text arXiv 1707.06143: pdf, ps.

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