Axiom Of Choice

We have the following indirect implication of form equivalence classes:

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

Implication	Reference
103 \(\Rightarrow\) 103	The Axiom of Choice, Jech, 1973b, page 164 problem 11.21

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

Howard-Rubin Number	Statement
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.
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.

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