Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 136-k
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 136-k

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.

136-k:

Surjective Cardinal Cancellation (depends on \(k\in\omega-\{0\}\)): For all cardinals \(x\) and \(y\), \(kx\le^* ky\) implies \(x\le^* y\).

Comment:

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