Abstract
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.
References
[1] IX latin american symposium on mathematical logic: Bahia blanca, 1992, The Journal of Symbolic Logic 59(2) (1994), 682-695.10.2307/2275422Search in Google Scholar
[2] R. Cignoli, Moisil algebras, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca, 1970, Notas de Lógica Matemática, No. 27.Search in Google Scholar
[3] P. M. Cohn, Universal Algebra, Harper & Row, Publishers, New York, Evanston, London, 1965.Search in Google Scholar
[4] A. V. Figallo, pn1q-valued implicative Łukasiewicz algebras with additional operations, Tesis Doctoral, Univ. Nac. del Sur, 1990.Search in Google Scholar
[5] A. V. Figallo, Free monadic Tarski algebras, Algebra Universalis 35(1) (1996), 141-150.10.1007/BF01190974Search in Google Scholar
[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.Search in Google Scholar
[7] P. R. Halmos, Free monadic algebras, Proc. Amer. Math. Soc. 10 (1959), 219-227.10.1090/S0002-9939-1959-0106198-3Search in Google Scholar
[8] A. Monteiro, On the definition of three-valued Łukasiewicz algebras, Bull. Math. 55(7) (1963), 3-12.Search in Google Scholar
[9] A. Monteiro, L. Iturrioz, Monadic Tarski algebras representation, Rev. Un. Mat. Argentina 19(5) (1962), 361.Search in Google Scholar
[10] A. Monteiro, L. Iturrioz, Monadic Tarski algebras representation, no. 76 in Informe técnico interno, INMABB - UNS - CONICET, Bahía Blanca, 2002.Search in Google Scholar
[11] L. Monteiro, Monadic three-valued Łukasiewicz algebras, Notas de Lógica Matemática, INMABB - UNS - CONICET, Bahía Blanca, 1974, 32.Search in Google Scholar
[12] L. F. Monteiro, M. Abad, S. Savini, J. Sewald, Free monadic Tarski algebras, Algebra Universalis 37 (1997), 106-118.10.1007/s000120050006Search in Google Scholar
[13] I. Viglizzo, Free monadic three-valued Łukasiewicz algebras, Rev. Un. Mat. Argentina 41(2) (1998), 109-117. Search in Google Scholar
© by Ignacio D. Viglizzo
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