Recall that for a given cardinal \(\displaystyle \kappa\), \(\displaystyle H(\kappa)\) denotes the collection of sets whose transitive closure has cardinality less than \(\displaystyle \kappa\). Prove that \(\displaystyle H(\aleph_1)\) has cardinality \(\displaystyle 2^{\aleph_0}\).
I am confused on how to prove this. I would appreciate some help on this problem. Thanks.
I am confused on how to prove this. I would appreciate some help on this problem. Thanks.