Philipp Hieronymi

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math.LO2024

A Cobham theorem for scalar multiplication

Philipp Hieronymi, Sven Manthe, Chris Schulz

Let $α, β \in R_{> 0}$ be such that $α, β$ are quadratic and $Q (α) \neq = Q (β)$ . Then every subset of $R^{n}$ definable in both $(\mathbb{R},{<},+,\mathb…

math.LO2010

Dependent Pairs

Ayhan Günaydin, Philipp Hieronymi

We prove that certain pairs of ordered structures are dependent. Among these structures are dense and tame pairs of o-minimal structures and further the real field with a multiplic…