Implications

We have the following indirect implication of form equivalence classes:

61 \(\Rightarrow\) 423
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
61 \(\Rightarrow\) 423 clear

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

Howard-Rubin Number Statement
61:

\((\forall n\in\omega, n\ge 2\))\((C(\infty,n))\): For each \(n\in\omega\), \(n\ge 2\), every set of \(n\) element  sets has a choice function.

423:

\(\forall n\in \omega-\{o,1\}\), \(C(\aleph_0, n)\) : For every \(n\in  \omega - \{0,1\}\), every denumerable set of \(n\) element sets has a choice function.

Comment:

Back