Implications

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We have the following indirect implication of form equivalence classes:

45-n \(\Rightarrow\) 45-n given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
45-n \(\Rightarrow\) 45-n	Axiom of choice for finite sets, Mostowski, A. 1945, Fund. Math. Finite axioms of choice, Truss, J. K. 1973a, Ann. Math. Logic

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

Howard-Rubin Number	Statement
45-n:	If \(n\in\omega-\{0,1\}\), \(C(\infty,n)\): Every set of \(n\)-element sets has a choice function.
45-n:	If \(n\in\omega-\{0,1\}\), \(C(\infty,n)\): Every set of \(n\)-element sets has a choice function.

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