Set theory MOC

Zorn's lemma

Zorn's lemma is a proposition of set theory that is equivalent to the Axiom of Choice and the Well ordering principle over .1

If is a partially ordered set in which every chain has an upper bound, then has a maximal element. #m/thm/set/zfc

Zorn's lemma may be weakened to the Ultrafilter lemma.

#state/develop | #lang/en | #SemBr

Footnotes

  1. 2008. Advanced Linear Algebra, p. 12 ↩