Implications

We have the following indirect implication of form equivalence classes:

130 \(\Rightarrow\) 389
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
130 \(\Rightarrow\) 79 clear
79 \(\Rightarrow\) 139
139 \(\Rightarrow\) 389

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

Howard-Rubin Number Statement
130:

\({\cal P}(\Bbb R)\) is well orderable.

79:

\({\Bbb R}\) can be well ordered.  Hilbert [1900], p 263.

139:

Using the discrete topology on 2, \(2^{\cal P(\omega)}\) is compact.

389:

\(C(\aleph_0,2,\cal P({\Bbb R}))\): Every denumerable family of two element subsets of \(\cal P({\Bbb R})\) has a choice function.  \ac{Keremedis} \cite{1999b}.

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