Modules over quantaloids: applications to the isomorphism problem in algebraic logic and π-institutions

Galatos, Nikolaos; Gil Férez, José (2017). Modules over quantaloids: applications to the isomorphism problem in algebraic logic and π-institutions. Journal of pure and applied algebra, 221(1), pp. 1-24. Elsevier 10.1016/j.jpaa.2016.05.012

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We solve the isomorphism problem in the context of abstract algebraic logic and of π-institutions, namely the problem of when the notions of syntactic and semantic equivalence among logics coincide. The problem is solved in the general setting of categories of modules over quantaloids. We introduce closure operators on modules over quantaloids and their associated morphisms. We show that, up to isomorphism, epis are morphisms associated with closure operators. The notions of (semi-)interpretability and (semi-)representability are introduced and studied. We introduce cyclic modules, and provide a characterization for cyclic projective modules as those having a g-variable. Finally, we explain how every π-institution induces a module over a quantaloid, and thus the theory of modules over quantaloids can be considered as an abstraction of the theory of π-institutions.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Galatos, Nikolaos and Gil Férez, José

Subjects:

500 Science > 510 Mathematics

ISSN:

0022-4049

Publisher:

Elsevier

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

17 Apr 2018 11:12

Last Modified:

24 Oct 2019 16:21

Publisher DOI:

10.1016/j.jpaa.2016.05.012

BORIS DOI:

10.7892/boris.109188

URI:

https://boris.unibe.ch/id/eprint/109188

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