Every non-empty partially-ordered set in which every chain has an upper bound contains a maximal element. Equivalent to AC over ZF.
Zorn's lemma
Related concepts
- Axiom of choice (AC)
- Poset / lattice foundations: reflexive-antisymmetric-transitive ≤ and join/meet
- Birkhoff HSP theorem: variety = class closed under H, S, P
- Free algebra F_V(X) and its universal mapping property
- Mal'tsev term t(x,y,z) = xy⁻¹z: residuals 0 in Z and S_3
- Haag's theorem: continuum-many unitarily inequivalent CCR representations (quantum)