Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 245
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 245

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

Howard-Rubin Number Statement
1:

\(C(\infty,\infty)\):  The Axiom of Choice: Every  set  of  non-empty sets has a choice function.

245:

There is a function \(f :\omega_1\rightarrow \omega^{\omega}_1\) such that for every \(\alpha\), \(0 < \alpha < \omega_1\), \(f(\alpha )\) is a function from \(\omega\) onto \(\alpha\).

Comment:

Back