Axiom Of Choice

We have the following indirect implication of form equivalence classes:

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

Implication	Reference
255 \(\Rightarrow\) 255

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

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