Implications

We have the following indirect implication of form equivalence classes:

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

Implication Reference
26 \(\Rightarrow\) 209 note-72

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

Howard-Rubin Number Statement
26:

\(UT(\aleph_{0},2^{\aleph_{0}},2^{\aleph_{0}})\): The union of denumerably many sets each of power \(2^{\aleph _{0}}\) has power \(2^{\aleph_{0}}\).

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.

Comment:

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