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

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 tra…