The possible values of critical points between varieties of lattices
Logic
2014-03-24 v3 Category Theory
Abstract
We denote by Conc(L) the 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 its dual, and such that every simple member of W contains a prime interval, we prove that there exists a bounded lattice A in V with at most aleph 2 elements such that Conc(A) is not isomorphic to Conc(B) for any B in W. The bound aleph 2 is optimal. As a corollary of our results, there are continuum many congruence classes of locally finite varieties of (bounded) modular lattices.
Keywords
Cite
@article{arxiv.1003.5742,
title = {The possible values of critical points between varieties of lattices},
author = {Pierre Gillibert},
journal= {arXiv preprint arXiv:1003.5742},
year = {2014}
}