Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 209
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 209

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.

209:

There is an ordinal \(\alpha\) such that for all \(X\), if \(X\) is a denumerable union of denumerable sets then \({\cal P}(X)\) cannot be partitioned into \(\aleph_{\alpha}\) non-empty sets.

Comment:

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