Implications

We have the following indirect implication of form equivalence classes:

266 \(\Rightarrow\) 263
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
266 \(\Rightarrow\) 263 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
266:

\(H(AS,P)\): Every antisymmetric relation contains \(\subseteq\)-maximal partially ordered subset.

263:

\(H(AS\&C,P)\): Every every relation \((X,R)\) which is antisymmetric and connected contains a \(\subseteq\)-maximal partially ordered subset.

Comment:

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