Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 334
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 334

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.

334:

\(MC(\infty,\infty,\hbox{ even})\): For every set \(X\) of  sets such that for all \(x\in X\), \(|x|\ge 2\), there is a function \(f\) such that  for every \(x\in X\), \(f(x)\) is a finite, non-empty subset of \(x\) and \(|f(x)|\) is even.

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