2016 | 25 | 1 | 35-49
Article title

On some extensions of the class of MV-algebras

Title variants
Languages of publication
In the present paper we will ask for the lattice L(MVEx) of subvarieties of the variety defined by the set Ex(MV) of all externally compatible identities valid in the variety MV of all MV-algebras. In particular, we will find all subdirectly irreducible algebras from the classes in the lattice L(MVEx) and give syntactical and semantical characterization of the class of algebras defined by P-compatible identities of MV-algebras.
Physical description
  • Department of Logic, Nicolaus Copernicus University in Toruń, Toruń, Poland,
  • Chang, C.C., “Algebraic analysis of many valued logics”, Transactions of the American Mathematical Society, 88 (1958): 467–490. DOI: 10.1090/S0002-9947-1958-0094302-9 and DOI: 10.2307/1993227
  • Chang, C.C., “A new proof of the completeness of Łukasiewicz axioms”, Transactions of the American Mathematical Society, 93 (1959): 74–80. DOI: 10.1090/S0002-9947-1959-0122718-1
  • Di Nola, A., and A. Lettieri, “Equational characterization of all varieties of MV-zlgebras”, Journal of Algebra, 221 (1999): 463–474.
  • Gajewska-Kurdziel, K., “On the lattice of some varieties defined by P-compatible identities”, Zeszyty Naukowe Uniwersytetu Opolskiego, Matematyka, 29 (1995): 45–47.
  • Grigolia, R., “Algebraic analysis of Łukasiewicz-Tarski’s n-valued logical systems”, pp. 81–92 in Selected Papers on Łukasiewicz Sentential Calcui, R. Wojcicki (ed.), Zakład Narodowy imienia Ossolińskich, Wydawnictwo Polskiej Akademii Nauk: Wrocław, Warszawa, Krakow, Gdańsk, 1977.
  • Hałkowska, K., “Lattice of equational theories of P-compatible varieties”, pp. 587–595 in Logic at Work. Essays dedicated to the memory of Helena Rasiowa, E. Orłowska (ed.), Springer: Heidelberg, New York, 1998.
  • Komori, Y., “Super-Lukasiewicz implicational logics”, Nagoya Mathematical Journal, 72 (1978): 127–133.
  • Komori, Y., “Super Łukasiewicz propositional logics”, Nagoya Mathematical Journal, 84 (1981): 119–133.
  • Łukasiewicz, J., “O logice trojwartosciowej”, Ruch filozoficzny, 5 (1920): 169–171.
  • Łukasiewicz, J., and A. Tarski, “Untersuchungen uber den Aussagenkalkül”, Comptes Rendus des séances de la Société des Sciences et des Lettres de Varsovie, 23 Classe iii (1930): 30–50.
  • Mruczek-Nasieniewska, K., “The varieties defined by P-compatible identities of modular ortholattices”, Studia Logica 95 (2010): 21–35. DOI: 10.1007/s11225-010-9255-5
  • Mundici, D., “Interpretation of AF CU-algebras in Lukasiewicz sentential calculus”, J. Funct. Anal., 65 (1986): 15–63.
  • Płonka, J., “P-compatible identities and their applications to classical algebras”, Math. Slovaca, 40, 1 (1990): 21–30.
  • Płonka, J., “Subdirectly irreducible algebras in varieties defined by externally compatible identities”, Studia Scientarium Hungaria, 27 (1992): 267–271.
  • Rose, A., and J.B. Rosser, “Fragments of many-valued statement calculi”, Trans. Amer. Math. Soc., 87 (1958): 1–53. DOI: 10.1090/S0002-9947-1958-0094299-1 and DOI: 10.2307/1993083
  • Rosser, J.B., and A.R. Turquette, “Axiom schemes for m-valued propositional calculi”, The Journal of Symbolic Logic, 10, 3 (1945): 61–82. MR13718,
  • Tarski, A., Logic, Semantic, Metamathematics, Oxford Univ. Press, 1956.
  • Wajsberg, M., “Aksjomatyzacja trojwartosciowego rachunku zdań”, Comptes rendue des seauces de la Societe des Sciences et des Lettres de Varsovie, Classe III, 24 (1931): 259–262.
  • Wajsberg, M,., “Beiträge zum Metaaussagenkalkül I”, Monatshefte für Mathematik und Physik 42 (1935): 221–242.
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.