Hypothesis: HR 0: \(0 = 0\).
Conclusion: HR 315:
\(\Omega = \omega_1\), where
\(\Omega = \{\alpha\in\hbox{ On}: (\forall\beta\le\alpha)(\beta=0 \vee (\exists\gamma)(\beta=\gamma+1) \vee\)
there is a sequence \(\langle\gamma_n: n\in\omega\rangle\) such that for each \(n\),
\(\gamma_n<\beta\hbox{ and } \beta=\bigcup_{n<\omega}\gamma_n.)\} \)
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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