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

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)


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


Zbl 0597.46059