Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 56
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 56

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.

56:

\(\aleph(2^{\aleph_{0}})\neq\aleph_{\omega}\). (\(\aleph(2^{\aleph_{0}})\) is Hartogs' aleph, the least \(\aleph\) not \(\le 2^{\aleph_{0}}\).)
Mathias [1979], p 125.

Comment:

Back