Some results on diagonal-free two-dimensional cylindric algebras

• Autorzy: Figallo M.
• Języki publikacji: EN

Abstrakty

EN

Formulas for computing the number of Df2-algebra structures that can be defined over Bn, where Bn is the Boolean algebra with n atoms, as well as the fine spectrum of Df2 are obtained. Properties of the lattice of all subvarieties of Df2, Lambda(Df 2), are exhibited. In particular, the poset Si fin(Df2) is described.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2011
• Tom: Vol. 46
• Strony: 3--15
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Figallo M.

• Departamento de Matematica Universidad Nacional del Sur 8000 Bahia Blanca, Argentina.,

Bibliografia

• [1] N. Bezhanishvili, Varieties of two-dimensional cylindric algebras. Part I: Diagonal-free case, Algebra Universalis, 48, 1 (2002), pp. 11–42.
• [2] B. Davey, On the lattice of subvarieties. Houston J. Math. 5(1979), pp. 183 – 192.
• [3] M. Figallo, Finite diagonal–free two–dimensional cylindric algebras, Log. J. IGPL.12, 6 (2004), pp. 509–523.
• [4] M. Figallo, Una Contribución sobre las algebras cilindricas libres de elementos diagonales de dimensión dos, Ms. Dissertation. Universidad Nacional del Sur, 2005.
• [5] L. Henkin, D. Monk and A. Tarski, Cylindric Algebras, Parts I & II, North-Holland,1971 & 1985.
• [6] B. Jónsson, Algebras whose congruence lattices are distributive, Math. Scand., 21(1967), pp. 110–121.
• [7] L. Monteiro, M. Abad, S. Savini, J. Sewald and M. Zander, Subalgebras of a finite monadic Boolean Algebra, Reports on Mathematical Logic, 40 (2006), pp. 199–206.
• [8] W. Taylor, The fine spectrum of a variety. Algebra Universalis 5 no. 2 (1975), pp. 263–303.