Hypothesis: HR 0: \(0 = 0\).
Conclusion: HR 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.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M10\) Derrick/Drake Model | Let \(\cal M\) be a model of \(ZF + GCH\). Add to \(\cal M\) generic functions \(f_n\) for each \(n\in\omega\), where \(f_n:\omega_n\to\cal P(\omega)\), but do not add \(\{f_n: n\in\omega\}\) |
Code: 3
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