We have the following indirect implication of form equivalence classes:

30 \(\Rightarrow\) 198
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
30 \(\Rightarrow\) 198 clear

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

Howard-Rubin Number Statement
30:

Ordering Principle: Every set can be linearly ordered.

198:

For every set \(S\), if the only linearly orderable subsets of \(S\) are the finite subsets of \(S\), then either \(S\) is finite or \(S\) has an amorphous subset.

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