Andréka, Hajnal and Madarász, Judit and Németi, István and Székely, Gergely (2023) Testing Definitional Equivalence of Theories via Automorphism Groups. THE REVIEW OF SYMBOLIC LOGIC. pp. 1-22. ISSN 1755-0203 (print); 1755-0211 (online)
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Abstract
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.
| Item Type: | Article |
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| Uncontrolled Keywords: | definitional equivalence of theories, first-order logic, automorphism group, ultraproduct, categorical equivalence of theories, many-dimensional definitional equivalence, Morita equivalence, category of models |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 30 Jan 2024 08:34 |
| Last Modified: | 15 Feb 2024 08:30 |
| URI: | https://real.mtak.hu/id/eprint/186626 |
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