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

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.

arXiv commentIn the current version, the abstract has undergone a minor modification

References in corpus (1)

• The Additive Structure of Integers with the Lower Wythoff Sequence