On a result of Gábor Czédli concerning congruence lattices of planar semimodular lattices

Abstract

A planar semimodular lattice is slim if it does not contain $M_3$ as a sublattice. An SPS lattice is a slim, planar, semimodular lattice. A recent result of Gábor Czédli proves that there is an eight element (planar) distributive lattice that cannot be represented as the congruence lattice of an SPS lattice. We provide a new proof.