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May 2020 Uniformly Bounded Arrays and Mutually Algebraic Structures
Michael C. Laskowski, Caroline A. Terry
Notre Dame J. Formal Logic 61(2): 265-282 (May 2020). DOI: 10.1215/00294527-2020-0004

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. "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

Information

Received: 1 April 2019; Accepted: 11 November 2019; Published: May 2020
First available in Project Euclid: 9 April 2020

zbMATH: 07222691
MathSciNet: MR4092535
Digital Object Identifier: 10.1215/00294527-2020-0004

Subjects:
Primary: 03C52
Secondary: 03C13

Rights: Copyright © 2020 University of Notre Dame

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Vol.61 • No. 2 • May 2020
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