Axiom Of Choice

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 339 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
1 \(\Rightarrow\) 339

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

Howard-Rubin Number	Statement
1:	\(C(\infty,\infty)\): The Axiom of Choice: Every set of non-empty sets has a choice function.
339:	Martin's Axiom \((\aleph_{0})\): Whenever \((P\le)\) is a non-empty, ccc quasi-order (ccc means every anti-chain is countable) and \({\cal D}\) is a family of \(\le\aleph_0\) dense subsets of \(P\), then there is a \({\cal D}\) generic filter \(G\) in \(P\).

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