Notes on the set of principal congruences of a finite lattice. I. Some preliminary results
George Grätzer, H. Lakser · arXiv (Cornell University) · 2017
In the second edition of the congruence lattice book, Problem 22.1 asks for a characterization of subsets $Q$ of a finite distributive lattice $D$ such that there is a finite lattice $L$ whose congruence lattice is isomorphic to $D$ and under this isomorphism $Q$ corresponds the the principal congruences of $L$. In this note, we prove some preliminary results.