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Internalising equality in Boolean algebras
journal contribution
posted on 2023-05-16, 12:04 authored by Fearnley-Sander, DP, Stokes, TEWe show that equality may be internalized in Boolean algebras, in a number of possible ways, as a binary operation satisfying reflexivity and replacement properties. The variety of equality Boolean rings is shown to be equivalent to the variety of modal rings (Boolean rings endowed with a generalised interior operator and important in modal logic). Varying the strength and exact nature of the replacement property corresponds to selecting from a number of natural varieties of modal rings. The work generalises a result of Suszko who considered the S4 case.
History
Publication title
Algebra UniversalisVolume
43Issue
2-3Pagination
187-195ISSN
0002-5240Department/School
School of Natural SciencesPublisher
Birkhauser VerlagPlace of publication
SwitzerlandRepository Status
- Restricted