Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 172
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 172

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.

172:

For every infinite set \(S\), if \(S\) is hereditarily countable  (that is, every \(y\in TC(S)\) is countable) then \(|TC(S)|= \aleph_{0}\).

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