Generalized semilattices and \(m\)-degrees of index sets. II (Q1803011)

[For part I see Algebra Logika 28, No. 5, 555-569 (1989; Zbl 0708.06005).] Let \(L\) be a semilattice. A congruence \(\theta\subseteq L\times L\) is called distributive if \(\theta(a)\leq \theta(b)\Rightarrow(\exists c\in \theta(a))(c\leq b)\), and is called countable if for each \(a\in L\) the class \(\theta(a)\) is at most countable. Theorem 1. Let \(L\) be a \(c\)- universal semilattice and \(\theta\) a countable congruence on \(L\). Then \(L/\theta\) is pseudo-\(c\)-universal. This result is applied to the generalized semilattice of the \(m\)-degrees of families of partial recursive functions or of their index sets.