Abstract
For non-trivial Heyting algebras H 1, H 2 one always has at least one homomorphism H 1 →H 2; if H 1 = H 2 there is at least one non-identical one. A Heyting algebra H is almost rigid if ∣ End(H)∣ = 2 and a system of almost rigid algebras ℌ is said to be discrete if ∣ Hom(H 1, H 2)∣ = 1 for any two distinct H 1, H 2 ∈ ℌ. We show that there exists a discrete system of 2ω countable almost rigid Heyting algebras.
The second author would like to express his thanks for the support by the project LN 00A056 of the Ministry of Education of the Czech Republic.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. E. Adams, V. Koubek, and J. Sichler, Endomorphisms and homomorphisms of Heyting algebras, Algebra Universalis 20 (1985), 167–178.
R. Balbes, P. Dwinger, “Distributive Lattices”, University of Missouri Press, Columbia, Missouri, 1974.
B. Jónsson, A Boolean algebra without proper automorphisms, Proc. Amer. Math. Soc. 2 (1951), 766–770.
M. Katětov, Remarks on Boolean algebras, Colloq. Math. 2 (1951), 229–235.
S. Koppelberg, “Handbook of Boolean Algebras I”, North-Holland, Amsterdam, 1989.
C. Kuratowski, Sur la puissance de I’ensemble des “nombres de dimensions” de M. Fréchet, Fund. Math. 8 (1926), 201–208.
K. D. Magill, The semigroup of endomorphisms of a Boolean ring, Semigroup Forum 4 (1972), 411–416.
C. J. Maxson, On semigroups of Boolean ring endomorphisms, Semigroup Forum 4 (1972), 78–82.
H. A. Priestley, Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc. 2 (1970), 186–190.
H. A. Priestley, Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. 324 (1972), 507–530.
L. Rieger, Some remarks on automorphisms of Boolean algebras, Fund. Math. 38 (1951), 209–216.
B. M. Schein, Ordered sets, semilattices, distributive lattices, and Boolean algebras with homomorphic endomorphism semigroups, Fund. Math. 68 (1970), 31–50.
C. Tsinakis, Brouwerian Semilattices Determined by their Endomorphism Semigroups, Houston J. Math. 5 (1979), 427–436.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Adams, M.E., Pultr, A. (2006). Countable Almost Rigid Heyting Algebras. In: Klazar, M., Kratochvíl, J., Loebl, M., Matoušek, J., Valtr, P., Thomas, R. (eds) Topics in Discrete Mathematics. Algorithms and Combinatorics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33700-8_1
Download citation
DOI: https://doi.org/10.1007/3-540-33700-8_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33698-3
Online ISBN: 978-3-540-33700-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)