We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure . We prove that if is a complete -theory, then is mutually algebraic if and only if there is some model of for which every atomic formula has uniformly bounded arrays. Moreover, an incomplete theory is mutually algebraic if and only if every atomic formula has uniformly bounded arrays in every model of .
"Uniformly Bounded Arrays and Mutually Algebraic Structures." Notre Dame J. Formal Logic 61 (2) 265 - 282, May 2020. https://doi.org/10.1215/00294527-2020-0004