Adding a constant and an axiom to a doctrine

[en] 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.

Disciplines :

Mathematics

Author, co-author :

GUFFANTI, Francesca ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

External co-authors :

Language :

English

Title :

Adding a constant and an axiom to a doctrine

Publication date :

08 October 2024

Journal title :

Mathematical Logic Quarterly

ISSN :

0942-5616

eISSN :

1521-3870

Publisher :

John Wiley & Sons, United Kingdom

Peer reviewed :

Peer Reviewed verified by ORBi

Commentary :

47 pages

Available on ORBilu :

since 08 October 2024

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