Quasi-Polish spaces and spaces of filters in second-order arithmetic

Summary · qwen2.5:32b

The paper formalizes quasi-Polish spaces and their equivalent representations, such as UF spaces and $\mathbf{\Pi}_2^0$ subspaces of $\mathcal{P}(\mathbb{N})$, within second-order arithmetic to conduct a reverse mathematical analysis of the transitions between these structures. This work matters as it provides foundational insights into the logical strength required for equivalences among different representations of quasi-Polish spaces, enhancing understanding in descriptive set theory and topology.

Excerpt

arXiv:2605.15052v2 Announce Type: replace Abstract: The class of quasi-Polish spaces admits several equivalent representations, including UF spaces, NP spaces, $\mathbf{\Pi}_2^0$ 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.