Extendible: Difference between revisions
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Extendible cardinals are a powerful [[large cardinal]] notion, which can be considered a significant strengthening of [[Weakly compact cardinal|weakly compact cardinals]], or a combination of [[supercompact]] and superstrong cardinals. A cardinal \(\kappa\) is called \(\eta\)-extendible iff, for some \(\theta\), there is some elementary embedding \(j: V_{\kappa+\eta} \to V_\theta\) with critical point \(\kappa\). We say \(\kappa\) is extendible iff it is \(\eta\)-extendible for all \(\eta > 0\). This is equivalent to a form of second-order infinitary compactness, or one of the two following other elementary embedding characterisations:
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