Implications

We have the following indirect implication of form equivalence classes:

130 \(\Rightarrow\) 70
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
130 \(\Rightarrow\) 79 clear
79 \(\Rightarrow\) 70 clear

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.

70:

There is a non-trivial ultrafilter on \(\omega\). Jech [1973b], prob 5.24.

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