A Cobham theorem for scalar multiplication

Philipp Hieronymi, Sven Manthe, Chris Schulz

Let $\hat{I}\pm ,{\hat{I}}^2\in {\mathbb{R}}_{>0}$ be such that $\hat{I}\pm ,{\hat{I}}^2$ are quadratic and $\mathbb{Q}(\hat{I}\pm )\ne \mathbb{Q}({\hat{I}}^2)$. Then every subset of ${\mathbb{R}}^n$ definable in both $(\mathbb{R},{<},+,…