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Functional Monadic Bounded Algebras

Robert Goldblatt
Studia Logica: An International Journal for Symbolic Logic
Vol. 96, No. 1 (October 2010), pp. 41-48
Published by: Springer
Stable URL: http://www.jstor.org/stable/40927706
Page Count: 8
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Functional Monadic Bounded Algebras
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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 ∃ 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 ∃E = 1 and ∃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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