Abstract. We prove that the lattice $\mathop{\rm Eq} \Omega $ of all equivalence relations on an infinite set $\Omega $ 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 $\mathop{\rm Eq} \Omega $ also contains, as a sublattice, the coproduct of $2^{\mathop{\rm card}\Omega }$ copies of itself.
AMS Subject Classification
(1991): 06B15; 06B10, 06B25
Keyword(s):
Lattice,
equivalence relation,
embedding,
coproduct,
ideal,
filter,
upper continuous
Received October 1, 2007. (Registered under 6444/2009.)
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