Zero sharp: Difference between revisions
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RhubarbJayde (talk | contribs) (Created page with "Zero sharp is a sharp for the constructible universe \(L\), which is of importance in inner model theory. Zero sharp, denoted \(0^\sharp\), if it exists, is a real number which encodes information about indiscernibles in the constructible universe. In particular, "\(0^\sharp\) exists" is the assertion that there is a unique class \(I\) of ordinals which is club in \(\mathrm{Ord}\), containing all uncountable cardinals so that, for every un...") |
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* There is an uncountable set \(X\) of ordinals with no \(Y \in L\) so that \(X \subseteq Y\) and \(|X| = |Y|\) (Jensen's covering theorem fails).
* For all \(\alpha\), \(|V_\alpha \cap L| = |L_\alpha|\).
* Every game whose payoff set is a \(\Sigma^1_1\) subset of Baire space is [[Axiom of determinacy|determined]].
* \(\aleph_\omega^V\) is regular in \(
* There is a nontrivial elementary embedding \(j: L \to L\).
* There is a proper class of nontrivial elementary embedding \(j: L \to L\), all with different critical points.
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