Abstract
We study the model theoretic structure (Z,+,Pr) where r>1 is an irrational number and the elements of Pr are of the form ⌊nr⌋ for some n∈Z∖{0}. We axiomatize 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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