Implications

We have the following indirect implication of form equivalence classes:

203 \(\Rightarrow\) 369
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
203 \(\Rightarrow\) 369 Non-constructive properties of the real numbers, Howard, P. 2001, Math. Logic Quart.

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
203:

\(C\)(disjoint,\(\subseteq\Bbb R)\): Every partition of \({\cal P}(\omega)\) into non-empty subsets has a choice function.

369:

If \(\Bbb R\) is partitioned into two sets, at least one of them has cardinality \(2^{\aleph_0}\).

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