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We have the following indirect implication of form equivalence classes:

130 \(\Rightarrow\) 289 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
130 \(\Rightarrow\) 79	clear
79 \(\Rightarrow\) 289	clear

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

Howard-Rubin Number	Statement
130:	\({\cal P}(\Bbb R)\) is well orderable.
79:	\({\Bbb R}\) can be well ordered.  Hilbert [1900], p 263.
289:	If \(S\) is a set of subsets of a countable set and \(S\) is closed under chain unions, then \(S\) has a \(\subseteq\)-maximal element.

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