Introducing Boolean Semilattices

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2018_Bergman_IntroductingBooleanManuscript.pdf (250.61 KB)
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2018-03-21
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Bergman, Clifford
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Bergman, Clifford
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Mathematics
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Abstract

We present and discuss a variety of Boolean algebras with operators that is closely related to the variety generated by all complex algebras of semilattices. We consider the problem of finding a generating set for the variety, representation questions, and axiomatizability. Several interesting subvarieties are presented. We contrast our results with those obtained for a number of other varieties generated by complex algebras of groupoids.
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This is a manuscript of a chapter from Bergman C. (2018) Introducing Boolean Semilattices. In: Czelakowski J. (eds) Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science. Outstanding Contributions to Logic, vol 16. Springer, Cham. doi: 10.1007/978-3-319-74772-9_4. Posted with permission.
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http://doi.org/10.1007/978-3-319-74772-9_4
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https://dr.lib.iastate.edu/handle/20.500.12876/54584
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Algebra
Logic and Foundations
Mathematics
Keywords
Boolean algebra, BAO, semilattice, Boolean semilattice, Boolean groupoid, canonical extension, equationally definable principal congruence
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Mon Jan 01 00:00:00 UTC 2018
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