Implications

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We have the following indirect implication of form equivalence classes:

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

Implication	Reference
57 \(\Rightarrow\) 64	Classes of Dedekind finite cardinals, Truss, J. K. 1974a, Fund. Math.

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

Howard-Rubin Number	Statement
57:	If \(x\) and \(y\) are Dedekind finite sets then either \(|x|\le |y|\) or \(|y|\le |x|\). Mathias [1979], p 125.
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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