Strong cardinal

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A cardinal $\kappa$ is strong if it is $\theta$-strong for every ordinal $\theta$, meaning that there is an elementary embedding $j:V\to M$ of the universe $V$ into a transitive proper class $M$, having critical point $\kappa$ and with $V_\theta\subset M$. One may without loss also suppose that $j(\kappa)\gt\theta$.




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