Timeline for Characterizing elementary embeddings of $L$ and $L_\alpha$ under 0#

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Jun 25, 2021 at 20:50	comment	added	Philip Welch		@Farmer: I do agree with you on the countable set version, I was too sweeping, and yes it properly completes the original question 2. (I should add that alpha (and beta) are uncountable.) Thank you!
Jun 25, 2021 at 16:33	comment	added	Farmer S		I don't think the argument goes through for embeddings between sets (the variant of the question). In fact, let $\alpha$ be a limit ordinal and work in $L[G]$ where $G$ collapses $\iota_\alpha$ to $\omega$, and let $j:L_{\iota_\alpha}\to L_{\iota_\alpha}$ be elementary with $j\in L[G]$ and $\mathrm{crit}(j)=\iota_0$. Let $\left<\kappa_n\right>_{n<\omega}$ be the critical sequence of $j$. Then there is $n$ such that $\kappa_n$ is not an indiscernible: otherwise, since $\left<\kappa_n\right>_{n<\omega}\in L[G]$, we get $0^\#\in L[G]$. @PhilipWelch
Jun 2, 2014 at 13:22	history	answered	Philip Welch	CC BY-SA 3.0