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Embedding coproducts of partition lattices

Authors
  • Wehrung, Friedrich
Type
Preprint
Publication Date
Oct 15, 2007
Submission Date
Sep 27, 2007
Source
arXiv
License
Unknown
External links

Abstract

We prove that the lattice Eq(X) of all equivalence relations on an infinite set X contains, as a 0,1-sublattice, the 0-coproduct of two copies of itself, thus answering a question by G.M. Bergman. Hence, by using methods initiated by de Bruijn and further developed by Bergman, we obtain that Eq(X) also contains, as a sublattice, the coproduct of 2^{card(X)} copies of itself.

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