Submission date: 4 October 2021

Abstract:

We introduce a complete axiomatization for the structure Z_α=(Z, +, 0, 1, f) where f : x → ⌊ α x ⌋ is a unary function with α a fixed transcendental number. This result fits into the more general theme of adding traces of multiplication to integers without losing decidability. When α is either a quadratic number or an irrational number less than one, similar decidability results have been already obtained by applying heavy techniques from the theory of autamota. Nevertheless, our approach is based on a clear axiomatization and involves only elementary techniques from model theory.

Mathematics Subject Classification: Primary 03B25, Secondary 03C10, 11U09, 11U05

Keywords and phrases:

Full text arXiv 2110.01673: pdf, ps.