Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 207-alpha
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 207-alpha

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.

207-alpha:

\(UT(\aleph_{\alpha },\aleph_{\alpha}, <2^{\aleph_{\alpha }})\): The union of \(\aleph_{\alpha}\) sets each of cardinality \(\aleph_{\alpha}\) has cardinality less than \(2^{\aleph_{\alpha}}\).

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