Every lattice has a cofinal totally ordered subset?
If a lattice is countable, prove that it has a subset that is both totally
ordered and cofinal in the lattice. Cofinal means that for each $l$ in the
lattice, there is some $a$ in the subset such that $l\le a$.
My idea was to try to use Zorn's lemma on the set of all totally ordered
subsets and prove it has a maximal element which must be cofinal, but this
hasn't helped much.
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