Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 103
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 103

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

Howard-Rubin Number Statement
1:

\(C(\infty,\infty)\):  The Axiom of Choice: Every  set  of  non-empty sets has a choice function.

103:

If \((P,<)\) is a linear ordering and \(|P| > \aleph_{1}\) then some initial segment of \(P\) is uncountable. Jech [1973b], p 164 prob 11.21.

Comment:

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