The Complete Congruence Lattice of a Complete Lattice
G. Birkhoff  raised the following question in 1945: Is every complete lattice isomorphic to the lattice of congruence relations of a suitable (infinitary) algebra? In 1948, Birkhoff restated this question in the Second Edition of his Lattice Theory ; however, “(infinitary)” was dropped from the question. This was intentional; G. Birkhoff referred to some continuity conditions that must hold in a congruence lattice of a (finitary) algebra.
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