Inter-model sets in Rd are model sets

Abstract

We show that any union of finitely many shifted model sets from a given cut-and-project scheme is a model set in some modified cut-and-project scheme. Restricting to direct space $R^d$, we show that any inter-model set is a model set in some modified cut-and-project scheme with second countable internal space. In both cases, the window in the modified cut-and-project scheme inherits the topological and measure-theoretic properties of the original windows.