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Preprint Number 1860

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1860. Ayhan Günaydın and Melissa Özsahakyan
Expansions of the Group of Integers by Beatty Sequences
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Submission date: 21 October 2020

Abstract:

We study the model theoretic structure (Z,+,P_r) where r>1 is an irrational number and the elements of P_r are of the form \floor{nr} for some nonzero integer n. We axiomatize of this structure and prove a quantifier elimination result. As a consequence we get that definable subsets are not sparse unless they are finite.

Mathematics Subject Classification: 03C07, 03C10

Keywords and phrases:

Full text arXiv 2010.10441: pdf, ps.


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