Journal article
Internalizing equality in Boolean algebras
Algebra Universalis, Vol.43(2-3), pp.187-196
2000
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.
Details
- Title
- Internalizing equality in Boolean algebras
- Authors/Creators
- D. Fearnley-Sander (Author/Creator) - University of TasmaniaT. Stokes (Author/Creator) - Murdoch University
- Publication Details
- Algebra Universalis, Vol.43(2-3), pp.187-196
- Publisher
- Springer
- Identifiers
- 991005540511007891
- Copyright
- © 2000 Birkhäuser Verlag Basel
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
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- Collaboration types
- Domestic collaboration
- Citation topics
- 9 Mathematics
- 9.280 Algebra & Topology
- 9.280.1047 Algebraic Logic
- Web Of Science research areas
- Mathematics
- ESI research areas
- Mathematics