On embedding of repetitive Meyer multiple sets into model multiple sets

Model sets are always Meyer sets but the converse is generally not true. In this work we show that for a repetitive Meyer multiple set of R-d with associated dynamical system. (X, R-d), the property of being a model multiple set is equivalent to (X, R-d) being almost automorphic. We deduce this by showing that a repetitive Meyer multiple set can always be embedded into a repetitive model multiple set having a smaller group of topological eigenvalues.