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TESTING DEFINITIONAL EQUIVALENCE OF THEORIES VIA AUTOMORPHISM GROUPS
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Journal Article
TESTING DEFINITIONAL EQUIVALENCE OF THEORIES VIA AUTOMORPHISM GROUPS
2024
Overview
Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and Pearce. In Example 2, uncountably many pairs of definitionally inequivalent theories are given such that their model categories are concretely isomorphic via bijections that preserve ultraproducts in the model categories up to isomorphism. Based on these results, we settle several conjectures of Barrett, Glymour and Halvorson.
Publisher
Cambridge University Press
Subject
