Monadic and closure MV-algebras. (English) Zbl 0920.06004

Georgescu, George; Iorgulescu, Afrodita; Leuştean, Ioana

Mult.-Valued Log. 3, No. 3, 235-257 (1998).

Introduced by C. C. Chang, MV-algebras are the Lindenbaum algebras of the infinite-valued calculus of Łukasiewicz [see D. Mundici, “Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus”, J. Funct. Anal. 65, 15-63 (1986; Zbl 0597.46059), for further results]. Idempotent MV-algebras coincide with Boolean algebras. Monadic MV-algebras are a generalization of monadic Boolean algebras. Closure Boolean algebras are the Lindenbaum algebras of the propositional modal logic S4. The authors define the appropriate MV-algebraic generalization also of this notion, and analyze their deep connections. They also prove that, for \(n=3\) and 4, monadic \(\text{MV}_n\) algebras are equivalent to monadic \(n\)-valued Łukasiewicz-Moisil algebras.

Reviewer: D.Mundici (Milano)

MSC:

06D30	De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
06F20	Ordered abelian groups, Riesz groups, ordered linear spaces
03G25	Other algebras related to logic

Keywords:

monadic MV-algebras; closure MV-algebras; Lindenbaum algebras

Citations:

Zbl 0597.46059