Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 124
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 124

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.

124:

Every operator on a Hilbert space with an amorphous base is the direct sum of a finite matrix and  a  scalar operator.  (A set is amorphous if it is not the union of two disjoint infinite sets.)

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