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arXiv · 1803.10054

Uniformly bounded arrays and mutually algebraic structures

Michael C. Laskowski·Caroline A. Terry
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Abstract

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 $T$.

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Michael C. Laskowski, Caroline A. Terry. 2018-03-27. Uniformly bounded arrays and mutually algebraic structures. https://doi.org/10.1215/00294527-2020-0004

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