Projectivity and unication problem in the variety generated by monadic perfect MV -algebras

Antonio Di Nola, Revaz Grigolia, Ramaz Liparteliani


A description and characterization of free and projective monadic
MV -algebras in the variety generated by monadic perfectMV -algebras is given. It is proven that the variety generated by monadic perfect MV -algebras has unitary unication type.


MV -algebras, monadicMV -algebras, perfect MV -algebras, unication.


L. P. Belluce, Further results on innite valued predicate logic, J. Symbolic

Logic 29 (1964) 69-78.

H. Bass, Finite monadic algebras, Proceedings of the American Mathematical

Society, vol.9 (1958), pp. 258-268.

L. P. Belluce, C.C. Chang, A weak completeness theorem for innite

valued 2rst-order logic, J. Symbolic Logic 28 (1963) 43-50.

L. P. Belluce, A. Di Nola, B. Gerla, Perfect MV -algebras and their

Logic, Applied Categorical Structures Volume 15, Numbers 1-2 (2007),


L.P. Belluce, R. Grigolia and A. Lettieri Representations of monadic

MV- algebras, Studia Logica, vol. 81, Issue October 15th, 2005, pp.


C. C. Chang, Algebraic Analysis of Many-Valued Logics, Trans. Amer.

Math. Soc., 88(1958), 467-490.

A. Di Nola, R. Grigolia, On Monadic MV-algebras, APAL, Vol. 128,

Issues 1-3 (August 2004), pp. 125-139.

A. Di Nola, R. Grigolia, Projective MV-Algebras and Their Automorphism

Groups, J. of Mult.-Valued Logic & Soft Computing., Vol. 9

(2003), pp. 291-317.

A. Di Nola, R. Grigolia, Gdel spaces and perfect MV-algebras,

Journal of Applied Logic, Volume 13, Issue 3, 2015, pp. 270284.

A. Di Nola, A. Lettieri, Perfect MV-algebras are Categorically Equivalent

to Abelian `-Groups, Studia Logica, 53(1994), 417-432.

S. Ghilardi, Unication through projectivity, J. Logic Comput.,

(6),733-752, 1997.

S. Ghilardi, Unication, nite duality and projectivityin varieties of

Heyting algebras, APAL, 127,99-115, 2004.

G. Georgescu, A. Iurgulescu, I. Leustean, Monadic and Closure MVAlgebras,

Multi. Val. Logic 3 (1998) 235-257.

R. Grigolia, Free algebras of non-classical logics, Monograph, "Metsniereba",

Tbilisi, 110 pp.(1987) (Russian) (Math. Review: 89c: 00008)

R. Grigolia, Finitely generated free S4:3-algebras, Studies on nonclassical

logics and formal systems, Nauka, Moscow, 281 286 (1983)


L.S. Hay, An axiomatization of the innitely many-valued calculus, M.S.

Thesis, Cornell University, 1958.

J. Lukasiewicz, A. Tarski, Untersuchungen uber den Aussagenkalkul,

Comptes Rendus des seances de la Societe des Sciences et des Lettres

de Varsovie 23 (cl iii) (1930) 30-50.

R. McKenzie, An algebraic version of categorical equivalence for varieties

and more general algebraic categories, pp. 221-243, in Logic and Algebra,

edited by P. Agliano and A. Ursini, volume 180 of Lectures Notes in Pure

and Applied Mathematics, Marcel Dekker, Dedicated to Roberto Magari,

D. Mundici, Interpretation of AF C-Algebras in Lukasiewicz Sentential

Calculus, J. Funct. Analysis 65, (1986), 15-63.

R. W. Quackenbush, Demi-Semi-Primal Algebras and Malcev-Type

Conditions, Mathematische Zeithschrift vol.122, 1971, pp. 177188.

J.D. Rutledge, A preliminary investigation of the innitely many-valued

predicate calculus, Ph.D. Thesis, Cornell University, 1959.

B. Scarpellini, Die Nichtaxiomatisierbarkeit des unendlichwertigen

Pradikaten-kalkul von Lukasiewicz, J. Symbolic Logic 27 (1962) 159-170.

D. Schwartz, Theorie der polyadischen MV-Algebren endlicher Ordnung,

Math. Nachr. 78 (1977) 131-138.

D. Schwartz, Polyadic MV-algebras, Zeit. f. math. Logik und Grundlagen

d. Math. 26 (1980) 561-564.


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