Axiom Of Choice

We have the following indirect implication of form equivalence classes:

215 \(\Rightarrow\) 64 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
215 \(\Rightarrow\) 83	clear
83 \(\Rightarrow\) 64	The Axiom of Choice, Jech, 1973b, page 52 problem 4.10

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.
83:	\(E(I,II)\) Howard/Yorke [1989]: \(T\)-finite is equivalent to finite.
64:	\(E(I,Ia)\) There are no amorphous sets. (Equivalently, every infinite set is the union of two disjoint infinite sets.)

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