Expansions of the Group of Integers by Beatty Sequences

2020/10/20 by Günaydın, Ayhan, Özsahakyan, Melissa
#Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2010.10441

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 \floornr for some n∈\Z∖\0\. 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. We also prove that there are no reducts of this structure expanding (\Z,+).

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