Implications

We have the following indirect implication of form equivalence classes:

56 \(\Rightarrow\) 56
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
56 \(\Rightarrow\) 56 A survey of recent results in set theory, Mathias, A.R.D. 1979, Period. Math. Hungar.

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

Howard-Rubin Number Statement
56:

\(\aleph(2^{\aleph_{0}})\neq\aleph_{\omega}\). (\(\aleph(2^{\aleph_{0}})\) is Hartogs' aleph, the least \(\aleph\) not \(\le 2^{\aleph_{0}}\).)
Mathias [1979], p 125.

56:

\(\aleph(2^{\aleph_{0}})\neq\aleph_{\omega}\). (\(\aleph(2^{\aleph_{0}})\) is Hartogs' aleph, the least \(\aleph\) not \(\le 2^{\aleph_{0}}\).)
Mathias [1979], p 125.

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