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arXiv · 2605.15052

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

Yuzuki Kaneko·Keita Yokoyama
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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.

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Yuzuki Kaneko, Keita Yokoyama. 2026-05-14. Quasi-Polish spaces and spaces of filters in second-order arithmetic. https://arxiv.org/abs/2605.15052

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