The possible values of critical points between varieties of lattices
نویسندگان
چکیده
We denote by Conc L the (∨, 0)-semilattice of all finitely generated congruences of a lattice L. For varieties (i.e., equational classes) V and W of lattices such that V is contained neither in W nor in its dual, and such that every simple member of W contains a prime interval, we prove that there exists a bounded lattice A ∈ V with at most א2 elements such that Conc A is not isomorphic to Conc B for any B ∈ W. The bound א2 is optimal. As a corollary of our results, there are continuum many congruence classes of locally finite varieties of (bounded) modular lattices.
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