Quasi-Polish spaces and spaces of filters in second-order arithmetic
The class of quasi-Polish spaces admits several equivalent representations, including UF spaces, NP spaces, $\mathbfΠ_2^0$ subspaces of $\mathcal{P}(\mathbb{N})$, and sober spaces of countably presented frames. In this paper, we formalize these structures within second-order arithmetic and conduct a systematic reverse mathematical analysis of the transitions between them.
math.LO↗