Uniformly Bounded Arrays and Mutually Algebraic Structures
Michael Chris Laskowski, C. Terry · Notre Dame Journal of Formal Logic · 2020
We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure M. We prove that if T is a complete L-theory, then T is mutually algebraic if and only if there is some model M of T for which every atomic formula has uniformly bounded arrays. Moreover, an incomplete theory T is mutually algebraic if and only if every atomic formula has uniformly bounded arrays in every model M of T.