Notes on quasi-metrizability and trees - Nyikos, Peter (Topology Proceedings, 2023)
Without trying to be comprehensive, this article introduces some necessary and sufficient conditions under which a tree is quasi-metrizable. Sufficient conditions include the concepts of Q-special and R-special, and necessary ones include height ≤ ω_1 and lack of uncountable branches. It is shown how a Souslin tree is not quasi-metrizable by using a forcing and absoluteness argument, and the same is done for a tree defined in ZFC.