Least upper bounds of nonempty well-ordered subsets suffice to guarantee fixed points for progressive self-maps on posets, yielding a maximality principle with weaker completeness assumptions.
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Bourbaki--Zorn Normal Forms for Maximality Arguments
Least upper bounds of nonempty well-ordered subsets suffice to guarantee fixed points for progressive self-maps on posets, yielding a maximality principle with weaker completeness assumptions.