Implications

We have the following indirect implication of form equivalence classes:

91 \(\Rightarrow\) 203
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
91 \(\Rightarrow\) 79 clear
79 \(\Rightarrow\) 203 clear

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
91:

\(PW\):  The power set of a well ordered set can be well ordered.

79:

\({\Bbb R}\) can be well ordered.  Hilbert [1900], p 263.

203:

\(C\)(disjoint,\(\subseteq\Bbb R)\): Every partition of \({\cal P}(\omega)\) into non-empty subsets has a choice function.

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