  For a class V of algebras, denote by Conc(V) the class of all semilattices
isomorphic to the semilattice Conc(A) of all compact congruences of A, for some
A in V. For classes V1 and V2 of algebras, we denote by crit(V1,V2) the
smallest cardinality of a semilattice in Conc(V1) which is not in Conc(V2) if
it exists, infinity otherwise. We prove a general theorem, with categorical
flavor, that implies that for all finitely generated congruence-distributive
varieties V1 and V2, crit(V1,V2) is either finite, or aleph_n for some natural
number n, or infinity. We also find two finitely generated modular lattice
varieties V1 and V2 such that crit(V1,V2)=aleph_1, thus answering a question by
J. Tuma and F. Wehrung.
