Implications

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We have the following indirect implication of form equivalence classes:

164 \(\Rightarrow\) 79 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
164 \(\Rightarrow\) 91	Dedekind-Endlichkeit und Wohlordenbarkeit, Brunner, N. 1982a, Monatsh. Math.
91 \(\Rightarrow\) 79	clear

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

Howard-Rubin Number	Statement
164:	Every non-well-orderable set has an infinite subset with a Dedekind finite power set.
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.

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