A proof of Whitman’s representation theorem for finite lattices

Thomason, S. K.

doi:10.1090/S0002-9939-1970-0265234-9

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A proof of Whitman’s representation theorem for finite lattices
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by S. K. Thomason

Proc. Amer. Math. Soc. 25 (1970), 618-619

DOI: https://doi.org/10.1090/S0002-9939-1970-0265234-9

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Abstract:

The theorem to be proved states that every finite lattice is isomorphic to a sublattice of the lattice $\mathcal {E}(S)$ of all equivalence relations on a countable set $S$. Our proof combines concreteness with freedom from long routine computations.

References

Bjarni Jónsson, On the representation of lattices, Math. Scand. 1 (1953), 193–206. MR 58567, DOI 10.7146/math.scand.a-10377
Philip M. Whitman, Lattices, equivalence relations, and subgroups, Bull. Amer. Math. Soc. 52 (1946), 507–522. MR 16750, DOI 10.1090/S0002-9904-1946-08602-4