Every real $r\subset\omega$ is hereditarily countable, giving $2^{\aleph_0}\le|HC|$. Conversely each HC set is represented by a well-founded extensional relation on a subset of $\omega$; there are only $2^{\aleph_0}$ such relations. Hence equality.


Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 16J / f / Solution

 Solution (source code)