We have the following indirect implication of form equivalence classes:

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

Implication Reference
117 \(\Rightarrow\) 117 From accessible to inaccessible cardinals, Keisler-Tarski-1964[1964], Fund. Math.

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.

117:

If \(\kappa\) is a measurable cardinal, then \(\kappa\) is the \(\kappa\)th inaccessible cardinal.

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