Partition Representations of Free Lattices
نویسنده
چکیده
I. Introduction. If 5 is a set, we will denote by G>(S) the lattice of all partitions (equivalence relations) of S. Whitman [6] proved that any lattice L is isomorphic to a sublattice of (P(S) for some 5. His proof shows that, if L is infinite, we can take 5 to be no larger than L; for finite L, however, his proof only shows that 5 can be taken count-able. This leaves open the following (still unsolved) problem: can every finite lattice be embedded in the lattice of partitions of some finite set?
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