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A proof of Whitman's representation theorem for finite lattices

Author: S. K. Thomason
Journal: Proc. Amer. Math. Soc. 25 (1970), 618-619
MSC: Primary 06.30
MathSciNet review: 0265234
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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 [Enhancements On Off] (What's this?)

  • [1] Bjarni Jónsson, On the representation of lattices, Math. Scand. 1 (1953), 193-206. MR 15, 389. MR 0058567 (15:389d)
  • [2] Philip M. Whitman, Lattices, equivalence relations, and subgroups, Bull. Amer. Math. Soc. 52 (1946), 507-522. MR 8, 62. MR 0016750 (8:62b)

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Keywords: Representations of lattices, lattices of equivalence relations
Article copyright: © Copyright 1970 American Mathematical Society

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