Revision #358 → #1670 · back to history
addedZorn's lemma (statement)a5e78d6e9b95
addedHausdorff maximal principle (earlier formulation)c7da9006aea1
addedPartially ordered setd8fd74908ff6
addedGreater than or equal to30532ded1884
addedTotally ordered seta5a3225038b4
addedInherited order on a subset0d0d326cccd1
addedMaximal element45a37f9df4b4
addedTotally ordered set has at most one maximal elementd4993293b8e1
addedUpper boundf8d40d0deb5d
addedNonemptiness property is redundant9234a9c478a6
addedInductive set (Bourbaki)359c14e26993
addedZorn's lemma fails for a proper class2150c08c78ae
addedZorn's lemma (poset form)b59d53ff60dd
addedZorn's lemma (inductive set form)d74f75a6b4bf
addedCorollary (maximal element above a given element)7239d3d7453d
addedEvery vector space has a basis41d346c2b5ef
addedNontrivial ring with unity contains a maximal ideal56066d503386
addedTychonoff's theorem394764ce136c
addedTychonoff's theorem implies the axiom of choice5e919179b19f
addedEquivalent formulations of Zorn's lemmae915de6481a4
addedInflationary maps have fixed points (equivalent to Zorn)7db71d7a620d
addedStronger Zorn's lemma (well-ordered chains)d542d2f9e0b4
addedHausdorff maximal principle59c0f4a8ec10
addedLemma 1 (least upper bound form)d9d0783d884f
addedLemma 2 (subsets closed under unions)f2a703a7a543
addedZorn's lemma implies the axiom of choice50d58e6d94ab
addedZorn's lemma implies the well-ordering theoremb7f60e6f47d3
addedDcpo with least element has a maximal elementc1a9dd453edf
addedEquivalence with HMP, axiom of choice, well-ordering5989a92a3db8
addedEquivalent to strong completeness theorem31bee7fa1aa9
addedBanach's extension theorem / Hahn–Banach1887295a48cf
addedEvery vector space has a basis (equivalent)59e16a69cdeb
addedKrull's theorem (maximal ideal)c08d8196a3a5
addedTychonoff's theorem (equivalent)f23102ece162
addedEvery proper filter is contained in an ultrafilterf9855f2cef69
addedWeak Zorn under ZF+DC (finite chains)4ae386a155c9
addedZorn's lemma for preordered sets78e1e4e9ab32