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On intervals and chains in epimorphness skeletons of congruence- distributive varieties. (English. Russian original) Zbl 0760.08004

Algebra Logic 29, No. 2, 144-154 (1990); translation from Algebra Logika 29, No. 2, 207-219 (1990).
For a variety \(V\) denote by \(IV\) the class of isomorphism types of \(V\)- algebras. Write \(a\ll b\) if \(a,b\) are isomorphism types of two algebras \(A,B\) such that \(A\) is a homomorphic image of \(B\). The quasiordered class \((IV;\ll)\) is called the epimorphy skeleton of \(V\). The author studies the order types of intervals and maximal chains in epimorphy skeletons of congruence distributive varieties. It is proved that for any nontrivial congruence distributive variety \(V\), any quasiordered set can be embedded into \((IV;\ll)\). Under the continuum hypothesis, in the epimorphy skeleton of a nontrivial congruence distributive variety there exists a maximal chain which is isomorphic to the ordered set of real numbers. There are other results.
Reviewer: J.Ježek (Praha)

MSC:

08B10 Congruence modularity, congruence distributivity
03E50 Continuum hypothesis and Martin’s axiom
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References:

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