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BEYOND LINGUISTIC INTERPRETATION IN THEORY COMPARISON
Published online by Cambridge University Press: 21 December 2023
Abstract
This paper assembles a unifying framework encompassing a wide variety of mathematical instruments used to compare different theories. The main theme will be the idea that theory comparison techniques are most easily grasped and organized through the lens of category theory. The paper develops a table of different equivalence relations between theories and then answers many of the questions about how those equivalence relations are themselves related to each other. We show that Morita equivalence fits into this framework and provide answers to questions left open in Barrett and Halvorson [4]. We conclude by setting up a diagram of known relationships and leave open some questions for future work.
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- Research Article
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic