A <Kurepa tree> is a <set-theoretic tree> of height $\omega_1$, with every level countable, possessing at least $\aleph_2$ distinct <cofinal branches>. The predecessors of each node are well ordered; their <order type> is the node's height. A <cofinal branch> is a maximal chain with nodes at unbounded heights below $\omega_1$, equivalently one node at every level after taking its predecessor closure.

Solution

Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 24 / 2 / a / ii / Solution

 Solution (source code)