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arXiv · 2110.01673

Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence

Mohsen Khani·Ali N. Valizadeh·Afshin Zarei
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Abstract

We introduce a model-complete theory which completely axiomatizes the structure $Z_{\alpha}=(Z, +, 0, 1, f)$ where $f : x \to \lfloor{\alpha} x \rfloor $ is a unary function with $\alpha$ a fixed transcendental number. When $\alpha$ is computable, our theory is recursively enumerable, and hence decidable as a result of completeness. Therefore, this result fits into the more general theme of adding traces of multiplication to integers without losing decidability.

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Mohsen Khani, Ali N. Valizadeh, Afshin Zarei. 2021-10-04. Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence. https://doi.org/10.1016/j.apal.2024.103493

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