A Cobham theorem for scalar multiplication

Philipp Hieronymi, Sven Manthe, Chris Schulz

Let $\alpha ,\beta \in {\mathbb{R}}_{>0}$ be such that $\alpha ,\beta$ are quadratic and $\mathbb{Q}(\alpha )\ne \mathbb{Q}(\beta )$. Then every subset of ${\mathbb{R}}^n$ definable in both $(\mathbb{R},{<},+,\mathb…