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Internalising equality in Boolean algebras

Citation

Fearnley-Sander, DP and Stokes, TE, Internalising equality in Boolean algebras, Algebra Universalis, 43, (2-3) pp. 187-195. ISSN 0002-5240 (2000) [Refereed Article]

DOI: doi:10.1007/s000120050152

Abstract

We 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.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Algebra and Number Theory
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Fearnley-Sander, DP (Mr Desmond Fearnley-Sander)
ID Code:18651
Year Published:2000
Web of Science® Times Cited:2
Deposited By:Mathematics
Deposited On:2000-08-01
Last Modified:2011-08-04
Downloads:0

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