Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 293
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 293

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.

293:

For all sets \(x\) and \(y\), if \(x\) can be linearly ordered and there is a mapping of \(x\) onto \(y\), then \(y\) can be linearly ordered.

Comment:

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