Implications

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We have the following indirect implication of form equivalence classes:

110 \(\Rightarrow\) 373-n given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
110 \(\Rightarrow\) 373-n	The vector space Kinna-Wagner Principle is equivalent to the axiom of choice, Keremedis, K. 2001a, Math. Logic Quart.

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

Howard-Rubin Number	Statement
110:	Every vector space over \(\Bbb Q\) has a basis.
373-n:	(For \(n\in\omega\), \(n\ge 2\).) \(PC(\aleph_0,n,\infty)\): Every denumerable set of \(n\)-element sets has an infinite subset with a choice function.

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