Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 54
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 54

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.

54:

For all infinite cardinals \(m\), \(m\) adj \(2^{m}\) implies \(m\) is an aleph.  
Note that \(m\) adj \(n\) iff \(m < n\) and \(\neg (\exists p) (m < p < n).\)
Mathias [1979] prob 1337, thm 1338 and prob 1339.

Comment:

Back