Implications

We have the following indirect implication of form equivalence classes:

261 \(\Rightarrow\) 256
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
261 \(\Rightarrow\) 256 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
261:

\(Z(TR,T)\): Every transitive relation \((X,R)\) in which every subset which is a tree has an upper bound, has a maximal element.

256:

\(Z(P,F)\): Every partially ordered set \((X,R)\) in which every forest \(A\) has an upper bound, has a maximal element.

Comment:

Back