Hypothesis: HR 0: \(0 = 0\).
Conclusion: HR 182:
There is an aleph whose cofinality is greater than \(\aleph_{0}\).
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M17\) Gitik's Model | Using the assumption that for every ordinal \(\alpha\) there is a strongly compact cardinal \(\kappa\) such that \(\kappa >\alpha\), Gitik extends the universe \(V\) by a filter \(G\) generic over a proper class of forcing conditions |
Code: 3
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