Implications

We have the following indirect implication of form equivalence classes:

209 \(\Rightarrow\) 209
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
209 \(\Rightarrow\) 209

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

Howard-Rubin Number Statement
209:

There is an ordinal \(\alpha\) such that for all \(X\), if \(X\) is a denumerable union of denumerable sets then \({\cal P}(X)\) cannot be partitioned into \(\aleph_{\alpha}\) non-empty sets.

209:

There is an ordinal \(\alpha\) such that for all \(X\), if \(X\) is a denumerable union of denumerable sets then \({\cal P}(X)\) cannot be partitioned into \(\aleph_{\alpha}\) non-empty sets.

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