On some extensions of the class of MV-algebras
DOI:
https://doi.org/10.12775/LLP.2015.010Słowa kluczowe
MV-algebra, variety, identity, P-compatible identity, equational base, subdirectly irreducible algebrasAbstrakt
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.Bibliografia
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, http://projecteuclid.org/euclid.jsl/1183391454
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.
Pobrania
Opublikowane
Jak cytować
Numer
Dział
Statystyki
Liczba wyświetleń i pobrań: 825
Liczba cytowań: 0
