Implications

We have the following indirect implication of form equivalence classes:

255 \(\Rightarrow\) 260
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
255 \(\Rightarrow\) 260 Variations of Zorn's lemma, principles of cofinality, and Hausdorff's maximal principle, Part I and II, Harper, J. 1976, Notre Dame J. Formal Logic

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
255:

\(Z(D,R)\): Every directed relation \((P,R)\) in which every ramified subset \(A\) has an upper bound, has a maximal element.

260:

\(Z(TR\&C,P)\): If \((X,R)\) is a transitive and connected relation in which every partially ordered subset has an upper bound, then \((X,R)\) has a maximal element.

Comment:

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