Abstract
The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator \({\exists}\) reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomorphic to ones whose elements are propositional functions.
We show that FMBA is characterised by the disjunction of the equations \({\exists}E = 1\) and \({{\exists}E = 0}\). We also define a weaker notion of “relatively functional” algebra, and show that every member of MBA is isomorphic to a relatively functional one.
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References
Akishev Galym, Robert Goldblatt: ‘Monadic bounded algebras’. Studia Logica 96(1), 1–40 (2010) (this issue)
Halmos, Paul R., Algebraic Logic, Chelsea, New York, 1962.
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Goldblatt, R. Functional Monadic Bounded Algebras. Stud Logica 96, 41–48 (2010). https://doi.org/10.1007/s11225-010-9271-5
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DOI: https://doi.org/10.1007/s11225-010-9271-5