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We have the following indirect implication of form equivalence classes:

117 \(\Rightarrow\) 320 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
117 \(\Rightarrow\) 319	clear
319 \(\Rightarrow\) 320	note-20

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

Howard-Rubin Number	Statement
117:	If \(\kappa\) is a measurable cardinal, then \(\kappa\) is the \(\kappa\)th inaccessible cardinal.
319:	Measurable cardinals are inaccessible.
320:	No successor cardinal, \(\aleph_{\alpha+1}\), is measurable.

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