Expansions of the Group of Integers by Beatty Sequences

Ayhan Günaydın; Melissa Özsahakyan

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arXiv · 2010.10441

Expansions of the Group of Integers by Beatty Sequences

Ayhan Günaydın·Melissa Özsahakyan

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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 $n\in\Z\setminus\{0\}$. 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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BibTeX RIS

Ayhan Günaydın, Melissa Özsahakyan. 2020-10-20. Expansions of the Group of Integers by Beatty Sequences. https://arxiv.org/abs/2010.10441

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