Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 234
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 234

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.

234:

There is a non-Ramsey set: There is a set \(A\) of infinite subsets of \(\omega\) such that for every infinite subset \(N\) of \(\omega\), \(N\) has a subset which is in \(A\) and a subset which is not in \(A\).

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