= Countable membership coding
{title2=$(D,R,n),\ D\subseteq\omega,\ R\subseteq D^2$}
A countable <well-founded relation> that is an <extensional relation> codes a transitive set through the <Mostowski collapse theorem>. Adding a distinguished point selects one decoded set. Every <hereditarily countable set> has such a code by enumerating its transitive membership ancestry. There are only continuum many codes. In <ZFC>, selecting least codes in a well-order gives an injection of the hereditarily countable sets into a set of size $2^{\aleph_0}$.
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