Implications

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We have the following indirect implication of form equivalence classes:

79 \(\Rightarrow\) 272 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
79 \(\Rightarrow\) 272	Models of set theory containing many perfect sets, Truss, J. K. 1974b, Ann. Math. Logic

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

Howard-Rubin Number	Statement
79:	\({\Bbb R}\) can be well ordered.  Hilbert [1900], p 263.
272:	There is an \(X\subseteq{\Bbb R}\) such that neither \(X\) nor \(\Bbb R - X\) has a perfect subset.

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