Discriminator varieties of double-Heyting algebras

• Autorzy: Taylor C. J.

Identyfikatory

DOI

10.4467/20842589RM.16.001.5278

• Języki publikacji: EN

Abstrakty

EN

We prove that a variety of double-Heyting algebras is a discriminator variety if and only if it is semisimple if and only if it has equationally denable principal congruences. The result also applies to the class of Heyting algebras with a dual pseudocomplement operation and to the class of regular double p-algebras.

Słowa kluczowe

EN

double-Heyting algebra; dual pseudocomplement; Heyting algebra with dual pseudocomplement; dually pseudocomplemented Heyting algebra; discriminator variety; semisimple algebra; EDPC

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2016
• Tom: Vol. 51
• Strony: 3--14
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Taylor C. J.

• Mathematics and Statistics La Trobe University Victoria 3086 Australia

Bibliografia

• [1] W. J. Blok and D. Pigozzi, On the structure of varieties with equationally definable principal congruences. I. Algebra Universalis 15 (1982), 195-227.
• [2] S. Burris and H. P. Sankappanavar, A course in universal algebra, vol. 78 of Graduate Texts in Mathematics. Springer, New York-Berlin, 1981.
• [3] T. Katriňāk, The structure of distributive double p-algebras. Regularity and congruences. Algebra Universalis 3 (1973), 238-246.
• [4] T. Kowalski, Varieties of tense algebras. Rep. Math. Logic 32 (1998), 53-95.
• [5] R. McKenzie and M. Valeriote, The structure of decidable locally finite varieties, vol. 79 of Progress in Mathematics. Birkhauser Boston, Inc., Boston, MA, 1989.
• [6] H. P. Sankappanavar, Heyting algebras with dual pseudocomplementation. Pacific J. Math. 117 (1985), 405{415.
• [7] J. C. Varlet, A regular variety of type < 2; 2; 1; 1; 0; 0 >. Algebra Universalis 2 (1972), 218-223.
• [8] H.Werner, Discriminator-algebras, vol. 6 of Studien zur Algebra und ihre Anwendungen. Akademie-Verlag, Berlin, 1978. Algebraic representation and model theoretic properties

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.