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We have the following indirect implication of form equivalence classes:

86-alpha \(\Rightarrow\) 196-alpha given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
86-alpha \(\Rightarrow\) 196-alpha	Successive large cardinals, Bull Jr., E. L. 1978, Ann. Math. Logic

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

Howard-Rubin Number	Statement
86-alpha:	\(C(\aleph_{\alpha},\infty)\): If \(X\) is a set of non-empty sets such that \(|X| = \aleph_{\alpha }\), then \(X\) has a choice function.
196-alpha:	\(\aleph_{\alpha}\) and \(\aleph_{\alpha+1}\) are not both measurable.

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