Implications

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We have the following indirect implication of form equivalence classes:

265 \(\Rightarrow\) 266 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
265 \(\Rightarrow\) 266	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
265:	\(H(A,TR)\): Every relation \((X,R)\) contains a \(\subseteq\)-maximal transitive subset.
266:	\(H(AS,P)\): Every antisymmetric relation contains \(\subseteq\)-maximal partially ordered subset.

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