Expansions of the Group of Integers by Beatty Sequences
Logic
2021-04-21 v2 Combinatorics
Abstract
We study the model theoretic structure where is an irrational number and the elements of are of the form for some . 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 .
Cite
@article{arxiv.2010.10441,
title = {Expansions of the Group of Integers by Beatty Sequences},
author = {Ayhan Günaydın and Melissa Özsahakyan},
journal= {arXiv preprint arXiv:2010.10441},
year = {2021}
}