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We have the following indirect implication of form equivalence classes:

289 \(\Rightarrow\) 0 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
289 \(\Rightarrow\) 0

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

Howard-Rubin Number	Statement
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.
0:	\(0 = 0\).

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