Implications

We have the following indirect implication of form equivalence classes:

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

Implication Reference
215 \(\Rightarrow\) 198 clear

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

Howard-Rubin Number Statement
215:

If \((\forall y\subseteq X)(y\) can be linearly ordered implies \(y\) is finite), then \(X\) is finite.

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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