Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 152
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 152

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.

152:

\(D_{\aleph_{0}}\): Every non-well-orderable set is the union of a pairwise disjoint, well orderable family of denumerable sets.  (See note 27 for \(D_{\kappa}\), \(\kappa\) a well ordered cardinal.)

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