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smallest ordinal $\alpha$ such that $L \cap P(L_\alpha)$ is uncountable

Discussion in 'Mathematics' started by Jesse Elliott, Aug 2, 2020 at 2:25 AM.

  1. Let $V$ denote the von Neumann universe and $L$ Gödel's constructible universe. For any set $X$, let $P(X)$ denote the power set of $X$.

    Assume that $0^\sharp$ exists (and ZFC).

    What is the smallest ordinal $\alpha$ such that $L \cap P(L_{\alpha})$ is uncountable? (If $V = L$, then $\alpha = \omega$, but if $0^\sharp$ exists, then $\alpha > \omega$.)

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