Title: Some preliminary results on the set of principal congruences of a finite lattice,
Abstract: 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.