Implications

We have the following indirect implication of form equivalence classes:

296 \(\Rightarrow\) 390
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
296 \(\Rightarrow\) 64 clear
64 \(\Rightarrow\) 390 clear

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

Howard-Rubin Number Statement
296:

Part-\(\infty\): Every infinite set is the disjoint union of infinitely many infinite sets.

64:

\(E(I,Ia)\) There are no amorphous sets. (Equivalently, every infinite set is the union of two disjoint infinite sets.)

390:

Every infinite set can be partitioned either into two infinite sets or infinitely many sets, each of which has at least two elements. Ash [1983].

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