Some Results on Diagonal-free Two-dimensional Cylindric Allgebras

Martín Figallo

Some Results on Diagonal-free Two-dimensional Cylindric Allgebras

Publication date: 15.12.2011

Reports on Mathematical Logic, 2011, Number 46, pp. 3 - 15

https://doi.org/10.4467/20842589RM.11.001.0279

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Some Results on Diagonal-free Two-dimensional Cylindric Allgebras

Abstract

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.

Keywords

diagonal–free two–dimensional cylindric algebra; finite algebras; lattice of subvarieties

References

[1] N. Bezhanishvili, Varieties of two-dimensional cylindric algebras. Part I: Diagonalfree 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 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.

Information

Information: Reports on Mathematical Logic, 2011, Number 46, pp. 3 - 15

DOI: https://doi.org/10.4467/20842589RM.11.001.0279

Article type: Original article

Titles:

Polish:

Some Results on Diagonal-free Two-dimensional Cylindric Allgebras

English:

Some Results on Diagonal-free Two-dimensional Cylindric Allgebras

Authors

Martín Figallo

The National University of South, Bahía Blanca, Provincia de Buenos Aires, República Argentina

Published at: 15.12.2011

Article status: Open

Licence: None

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Martín Figallo (Author) - 100%

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