Implications

We have the following indirect implication of form equivalence classes:

47-n \(\Rightarrow\) 374-n
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
47-n \(\Rightarrow\) 423 clear
423 \(\Rightarrow\) 374-n clear

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

Howard-Rubin Number Statement
47-n:

If \(n\in\omega-\{0,1\}\), \(C(WO,n)\): Every well ordered collection 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.

374-n:

\(UT(\aleph_0,n,\aleph_0)\) for \(n\in\omega -\{0,1\}\): The union of a denumerable set of \(n\)-element sets is denumerable.

Comment:

Back