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Algebra Universalis
Article . 1985 . Peer-reviewed
License: Springer TDM
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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Endomorphisms and homomorphisms of Heyting algebras

Authors: M. E. Adams; M. E. Adams; V. Koubek; V. Koubek; J. Sichler; J. Sichler;

Endomorphisms and homomorphisms of Heyting algebras

Abstract

The main theorem of the article under review is the result that the variety of Heyting algebras is 0-map universal [see \textit{A. Pultr}, \textit{V. Trnková}, ''Combinatorial, algebraic, and topological representation of groups (1980; Zbl 0418.18004), for an in depth treatment of this notion]. The proof uses heterogeneous chains and Priestley duality. As a corollary, the authors obtain the fact that for every cardinal \(\kappa \geq 2^{\omega}\) there exist \(2^{\kappa}\) non isomorphic Heyting algebras of cardinality \(\kappa\) having exactly two endomorphisms. This result becomes particularly interesting in comparison to the fact that every infinite Boolean algebra has uncountably many endomorphisms. Finally, the authors raise the question what happens if \(\omega \leq \kappa <2^{\kappa}\).

Keywords

heterogeneous chains, endomorphisms, Heyting algebras (lattice-theoretic aspects), Automorphisms and endomorphisms of algebraic structures, variety of Heyting algebras, 0-map universal, Priestley duality

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Average
Average
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