Timeline for What's the order type of the following set?

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Aug 30 at 9:55	history	edited	C7X	CC BY-SA 4.0	Important edit
May 23 at 22:20	history	edited	C7X	CC BY-SA 4.0	Adding reference and pointer to proof, with thanks to Andreas Blass's comment
May 23 at 15:31	comment	added	Andreas Blass		The Wikipedia statement has acquired a source, but it's easier to write a proof than to look up the source. Let $H$ be the hull in question, so $H\prec L_{\omega_1}$. Suppose $x\in y\in H$; we want to prove $x\in H$. Since $L_{\omega_1}$ satisfies "all sets are countable", so does $H$. So $H$ contains a function $f$ from $\omega$ onto $y$. Now $x=f(n)$ for some natural number $n$. Since $H$ contains both $f$ and $n$, it contains $f(n)$, as desired.
Aug 26, 2023 at 23:49	history	edited	C7X	CC BY-SA 4.0	Possibly poor sourcing
Aug 26, 2023 at 23:41	history	edited	C7X	CC BY-SA 4.0	added 314 characters in body
Aug 26, 2023 at 23:34	history	answered	C7X	CC BY-SA 4.0