If every chain in a nonempty partially ordered set has an upper bound, then the set has a maximal element.
Ancestors (5)
Incoming links (53)
- Almost disjointness number
- Chain in a partial order
- Extension theorem for field embeddings
- Flasque-kernel section-lifting lemma
- Minimal compact face argument
- Minimal subsystem
- Nilradical as the intersection of prime ideals
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- Prime ideal avoiding a multiplicative subset
- Propositional compactness theorem
- Ultrafilter lemma
- Uncountable-language proof of propositional completeness
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