Implications

We have the following indirect implication of form equivalence classes:

60 \(\Rightarrow\) 102
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
60 \(\Rightarrow\) 62 clear
62 \(\Rightarrow\) 102 The Axiom of Choice, Jech, 1973b, page 162 problem 11.12

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

Howard-Rubin Number Statement
60:

\(C(\infty,WO)\): Every set of non-empty, well orderable sets has a choice function.
Moore, G. [1982], p 125.

62:

\(C(\infty,< \aleph_{0})\):  Every set of non-empty finite  sets  has  a choice function.

102:

For all Dedekind finite cardinals \(p\) and \(q\), if \(p^{2} = q^{2}\) then \(p = q\). Jech [1973b], p 162 prob 11.12.

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