Zero sharp: Difference between revisions
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* \(\aleph_\omega^V\) is regular in \(L\). |
* \(\aleph_\omega^V\) is regular in \(L\). |
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* There is a nontrivial elementary embedding \(j: L \to L\).<ref>Many papers about 0 sharp</ref> |
* There is a nontrivial elementary embedding \(j: L \to L\).<ref>Many papers about 0 sharp</ref> |
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* There is a proper class of nontrivial elementary |
* There is a proper class of nontrivial elementary embeddings \(j: L \to L\), all with different critical points. |
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* For some \(\alpha, \beta\), there is a nontrivial elementary embedding \(j: L_\alpha \to L_\beta\) with critical point below \(|\alpha|\). |
* For some \(\alpha, \beta\), there is a nontrivial elementary embedding \(j: L_\alpha \to L_\beta\) with critical point below \(|\alpha|\). |
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* Every uncountable cardinal is inaccessible in \(L\). (Possible source? <ref>W. H. Woodin, [https://arxiv.org/abs/1605.00613 The HOD dichotomy], p.1</ref>) |
* Every uncountable cardinal is inaccessible in \(L\). (Possible source? <ref>W. H. Woodin, [https://arxiv.org/abs/1605.00613 The HOD dichotomy], p.1</ref>) |
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