{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T17:25:19Z","timestamp":1774977919404,"version":"3.50.1"},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T00:00:00Z","timestamp":1703116800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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.<\/jats:p>","DOI":"10.1017\/s1755020323000321","type":"journal-article","created":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T11:03:45Z","timestamp":1703156625000},"page":"819-859","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["BEYOND LINGUISTIC INTERPRETATION IN THEORY COMPARISON"],"prefix":"10.1017","volume":"17","author":[{"given":"TOBY","family":"MEADOWS","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2023,12,21]]},"reference":[{"key":"S1755020323000321_r21","first-page":"284","volume-title":"Logic in Tehran Proceedings of the Workshop and Conference on Logic, Algebra and Arithmetic","volume":"26","author":"Visser","year":"2006"},{"key":"S1755020323000321_r15","volume-title":"Set Theory: An Introduction to Independence Proofs","author":"Kunen","year":"2006"},{"key":"S1755020323000321_r22","first-page":"1","article-title":"When bi-interpretability implies synonymy","volume":"320","author":"Visser","year":"2014","journal-title":"Logic Group Preprint Series"},{"key":"S1755020323000321_r24","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/978-3-030-64187-0_18","volume-title":"Hajnal Andr\u00e9ka and Istv\u00e1n N\u00e9meti on Unity of Science: From Computing to Relativity Theory Through Algebraic Logic","author":"Weatherall","year":"2021"},{"key":"S1755020323000321_r13","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1086\/701047","article-title":"Definable categorical equivalence","volume":"86","author":"Hudetz","year":"2019","journal-title":"Philosophy of Science"},{"key":"S1755020323000321_r16","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1007\/s10992-018-9491-0","article-title":"On generalization of definitional equivalence to non-disjoint languages","volume":"48","author":"Lefever","year":"2019","journal-title":"Journal of Philosophical Logic"},{"key":"S1755020323000321_r7","volume-title":"Model Theory","author":"Chang","year":"1973"},{"key":"S1755020323000321_r4","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1017\/S1755020316000186","article-title":"Morita equivalence","volume":"9","author":"Barrett","year":"2016","journal-title":"Review of Symbolic Logic"},{"key":"S1755020323000321_r2","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1002\/malq.200410051","article-title":"Mutual definability does not imply definitional equivalence, a simple example","volume":"51","author":"Andr\u00e9ka","year":"2005","journal-title":"Mathematical Logic Quarterly"},{"key":"S1755020323000321_r3","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198568612.001.0001","volume-title":"Category Theory","author":"Awodey","year":"2006"},{"key":"S1755020323000321_r5","first-page":"185","volume-title":"S\u00e9minaire de G\u00e9om\u00e9trie Alg\u00e9brique du Bois Marie - 1963-64 - Th\u00e9orie Des Topos et Cohomologie \u00e9tale Des sch\u00e9mas - (SGA 4) - Vol. 1 (Lecture Notes in Mathematics 269)","author":"Bourbaki","year":"1972"},{"key":"S1755020323000321_r10","first-page":"585","volume-title":"The Oxford Handbook of Philosophy of Science","author":"Halvorson","year":"2016"},{"key":"S1755020323000321_r8","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1017\/CBO9780511910616.004","volume-title":"Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies","author":"Enayat","year":"2011"},{"key":"S1755020323000321_r11","first-page":"402","volume-title":"Categories for the Working Philosopher","author":"Halvorson","year":"2018"},{"key":"S1755020323000321_r9","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/BFb0059148","volume-title":"Reports of the Midwest Category Seminar III","author":"Feferman","year":"1969"},{"key":"S1755020323000321_r14","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/BFb0063101","volume-title":"Category Seminar","author":"Kelly","year":"1974"},{"key":"S1755020323000321_r23","doi-asserted-by":"crossref","first-page":"e12592","DOI":"10.1111\/phc3.12592","article-title":"Part 1: Theoretical equivalence in physics","volume":"14","author":"Weatherall","year":"2019","journal-title":"Philosophy Compass"},{"key":"S1755020323000321_r17","volume-title":"Model Theory: And Introduction","author":"Marker","year":"2002"},{"key":"S1755020323000321_r6","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198790396.001.0001","volume-title":"Philosophy and Model Theory","author":"Button","year":"2018"},{"key":"S1755020323000321_r12","volume-title":"A Shorter Model Theory","author":"Hodges","year":"1997"},{"key":"S1755020323000321_r1","doi-asserted-by":"crossref","unstructured":"1 Andr\u00e9ka, H. , Madar\u00e1sz, J. , N\u00e9meti, I. , & Sz\u00e9kely, G. 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