Year: 2024
Type: preprint
Abstract: Let $α,β\in \mathbb{R}_{>0}$ be such that $α,β$ are quadratic and $\mathbb{Q}(α)\neq \mathbb{Q}(β)$. Then every subset of $\mathbb{R}^n$ definable in both $(\mathbb{R},{<},+,\mathbb{Z},x\mapsto αx)$ and $(\mathbb{R},{<},+,\mathbb{Z},x\mapsto βx)$ is already definable in $(\mathbb{R},{<},+,\mathbb{Z})$. As a consequence we generalize Cobham-Semenov theorems for sets of real numbers to $β$-numeration systems, where $β$ is a quadratic irrational.
Source: arXiv (Cornell University)
Institutions: University of Bonn, University of Waterloo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406072710