Free monadic Tarski and MMI3-algebras

• Autorzy: Entizne R. V. , Monteiro L. F. , Savini S. M. , Viglizzo I. D.
• Języki publikacji: EN

Abstrakty

EN

MMI3-algebras are a generalization of the monadic Tarski algebras as defined by A. Monteiro and L. Iturrioz, and a particular case of the MMIn+1-algebras defined by A. Figallo. They can also be seen as monadic three-valued Łukasiewicz algebras without a first element. By using this point of view, and the free monadic extensions, we construct the free MMI3-algebras on a finite number of generators, and indicate the coordinates of the generators. As a byproduct, we also obtain a construction of the free monadic Tarski algebras.

Słowa kluczowe

EN

Tarski algebra; MMI3-algebras; free algebras; monadic extension; generators

PL

algebra Tarskiego; algebra-MMI3; algebra wolna; generatory

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 3
• Strony: 509--521
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Entizne R. V.

• Departamento De Matemática, Universidad Nacional Del Sur Avda, Alem 1253 Bahía Blanca, Argentina

autor

Monteiro L. F.

• Departamento De Matemática, Universidad Nacional Del Sur Avda, Alem 1253 Bahía Blanca, Argentina

autor

Savini S. M.

• Departamento De Matemática, Universidad Nacional Del Sur Avda, Alem 1253 Bahía Blanca, Argentina

autor

Viglizzo I. D.

• Departamento De Matemática, Universidad Nacional Del Sur Avda, Alem 1253 Bahía Blanca, Argentina

Bibliografia

• [1] IX latin american symposium on mathematical logic: Bahia blanca, 1992, The Journal of Symbolic Logic 59(2) (1994), 682–695.
• [2] R. Cignoli, Moisil algebras, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca, 1970, Notas de Lógica Matemática, No. 27.
• [3] P. M. Cohn, Universal Algebra, Harper & Row, Publishers, New York, Evanston, London, 1965.
• [4] A. V. Figallo, (n+1)-valued implicative Łukasiewicz algebras with additional operations, Tesis Doctoral, Univ. Nac. del Sur, 1990.
• [5] A. V. Figallo, Free monadic Tarski algebras, Algebra Universalis 35(1) (1996), 141–150.
• [6] A. V. Figallo, A. Suardíaz, A. Ziliani, Free MMI3-algebras, in: Proceedings of the IX Latin American Symposium on Mathematical Logic, Part 2 (Bahía Blanca, 1992), vol. 39 of Notas Lógica Mat., Univ. Nac. del Sur, Bahía Blanca, 1994.
• [7] P. R. Halmos, Free monadic algebras, Proc. Amer. Math. Soc. 10 (1959), 219–227.
• [8] A. Monteiro, On the definition of three-valued Łukasiewicz algebras, Bull. Math. 55(7) (1963), 3–12.
• [9] A. Monteiro, L. Iturrioz, Monadic Tarski algebras representation, Rev. Un. Mat. Argentina 19(5) (1962), 361.
• [10] A. Monteiro, L. Iturrioz, Monadic Tarski algebras representation, no. 76 in Informe técnico interno, INMABB - UNS - CONICET, Bahía Blanca, 2002.
• [11] L. Monteiro, Monadic three-valued Łukasiewicz algebras, Notas de Lógica Matemática, INMABB - UNS - CONICET, Bahía Blanca, 1974, 32.
• [12] L. F. Monteiro, M. Abad, S. Savini, J. Sewald, Free monadic Tarski algebras, Algebra Universalis 37 (1997), 106–118.
• [13] I. Viglizzo, Free monadic three-valued Łukasiewicz algebras, Rev. Un. Mat. Argentina 41(2) (1998), 109–117.