= Kurepa tree from an inaccessible binary tree
{c}
Let $\kappa$ be <strongly inaccessible cardinal> in the ground model and perform the <finite Lévy collapse to omega-one>. The ground full binary <set-theoretic tree> of height $\kappa$ has all levels of size less than $\kappa$, so these levels become countable. Its at least $(\kappa^+)^M$ ground branches remain distinct. The <chain in a partial order> condition preserves $(\kappa^+)^M$, which is the extension $\aleph_2$. The unchanged ground <set-theoretic tree> therefore witnesses the <Kurepa hypothesis>.
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