Some Results on Diagonal-free Two-dimensional Cylindric Allgebras

Martín Figallo

Abstrakt

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, (Df 2), are exhibited. In particular, the poset Sifin(Df2) is described.

Słowa kluczowe: diagonal–free two–dimensional cylindric algebra, finite algebras, lattice of subvarieties
References
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[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 Contribucio´n sobre las ´algebras cil´ındricas libres de elementos diagonales de dimensio´n 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. J´onsson, 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.

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