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Quasi-Polish spaces and spaces of filters in second-order arithmetic
Abstract
The class of quasi-Polish spaces admits several equivalent representations, including UF spaces, NP spaces, Π20 subspaces of 𝒫(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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BibTeX
@misc{kaneko2026quasipolish,
title = {{Quasi-Polish spaces and spaces of filters in second-order arithmetic}},
author = {Yuzuki Kaneko and Keita Yokoyama},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.15052},
eprint = {2605.15052},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.15052},
}
RIS
TY - UNPB
TI - Quasi-Polish spaces and spaces of filters in second-order arithmetic
AU - Yuzuki Kaneko
AU - Keita Yokoyama
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2605.15052
UR - https://arxiv.org/abs/2605.15052
AB - The class of quasi-Polish spaces admits several equivalent representations, including UF spaces, NP spaces, Π_2^0 subspaces of 𝒫(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.
ER -