Adding a constant and an axiom to a doctrine
We study the meaning of “adding a constant to a language” for any doctrine, and “adding an axiom to a theory” for a primary doctrine, by showing how these are actually two instances of the same construction. We prove their universal properties, and how these constructions are compatible with additio...
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| Published in | Mathematical logic quarterly Vol. 70; no. 3; pp. 294 - 332 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Berlin
Wiley Subscription Services, Inc
01.08.2024
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| Online Access | Get full text |
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| Summary: | We study the meaning of “adding a constant to a language” for any doctrine, and “adding an axiom to a theory” for a primary doctrine, by showing how these are actually two instances of the same construction. We prove their universal properties, and how these constructions are compatible with additional structure on the doctrine. Existence of Kleisli object for comonads in the 2‐category of indexed poset is proved in order to build these constructions. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0942-5616 1521-3870 |
| DOI: | 10.1002/malq.202300053 |