Implications

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We have the following indirect implication of form equivalence classes:

272 \(\Rightarrow\) 169 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
272 \(\Rightarrow\) 169	clear

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

Howard-Rubin Number	Statement
272:	There is an \(X\subseteq{\Bbb R}\) such that neither \(X\) nor \(\Bbb R - X\) has a perfect subset.
169:	There is an uncountable subset of \({\Bbb R}\) without a perfect subset.

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