Answer by Brian M. Scott for what is $L_{\omega_1} (x)$?
When you see $L(x)$ or $L_\alpha(x)$, you’re dealing with relative constructibility. Instead of starting from the empty set ($L_0=\varnothing$), you start from $TC(x)$, the transitive closure of $x$...
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The class of all hereditarily countable sets can be proven to be a set from the axioms of Zermelo–Fraenkel set theory (ZF) without any form of the axiom of choice, and this set is designated . The...
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