Chris Schulz, Postdoc at the University of Waterloo
A Cobham theorem for scalar multiplication
The famous Cobham-Semenov theorem states that for k, l > 1 multiplicatively independent, if a subset of N^d is definable both using the base-k representations of its elements and using the base-l representations, then it is definable from only the addition function on N. We present an analogous result in the real case: for alpha, beta quadratic irrationals from distinct field extensions of Q, if a subset of R^d is definable by expanding the real ordered group with Z both using the multiplication by alpha and using the multiplication by beta, then it is definable from only the real ordered group with Z itself. This talk is based on joint work with Philipp Hieronymi and Sven Manthe.
MC 5403