Mutually algebraic structures and expansions by predicates

We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory T is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model M of T has an expansion ( M, A ) by a unary predicate with the finite cover property. We show that every structure has a maximal mutually algebraic reduct. and give a strong structure theorem for the class of elementary extensions of a fixed mutually algebraic structure.