Endomorphisms and homomorphisms of Heyting algebras (Q1061758)

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 \(\omega \leq \kappa <2^{\kappa}\).