Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 180
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 180

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.

180:

Every Abelian group has a divisible hull.  (If \(A\) and \(B\)  are groups, \(B\) is a divisible hull of \(A\) means \(B\) is a divisible group, \(A\) is a subgroup of \(B\) and for every non-zero \(b \in  B\), \(\exists  n \in \omega \)  such that \(0\neq nb\in A\).)  Fuchs [1970], Theorem 24.4 p 107.

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