Pith Number

pith:6JWCE2OP

pith:2026:6JWCE2OP4HGMXLNKAEBT7MP46M

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

Keita Yokoyama, Yuzuki Kaneko

Quasi-Polish spaces have equivalent representations as UF spaces, NP spaces, Π₂⁰ subspaces of P(N), and sober spaces of countably presented frames, all formalizable in second-order arithmetic.

arxiv:2605.15052 v1 · 2026-05-14 · math.LO

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Claims

C1strongest claim

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; these structures are formalized in second-order arithmetic and the transitions between them receive a systematic reverse-mathematical analysis.

C2weakest assumption

That the listed representations remain equivalent when interpreted inside the language and axioms of second-order arithmetic, without requiring extra set-existence principles beyond those already present in the base theory.

C3one line summary

Quasi-Polish spaces and their equivalent representations are formalized in second-order arithmetic, with reverse-mathematical analysis of the transitions between them.

References

11 extracted · 11 resolved · 0 Pith anchors

[1] Notions of closed subsets of a complete separa ble metric space in weak subsystems of second-order arithmetic 1987

[2] Quasi-Polish spaces 2013

[3] A generalization of a theorem of hurewicz fo r quasi- polish spaces 2018

[4] Ide al pre- sentations and numberings of some classes of eﬀective quasi-Polish spaces 2024

[5] Spatiality of countably presentable locales (p roved with the baire category theorem) 2015

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:38:54.378008Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f26c2269cfe1cccbadaa01033fb1fcf328b8828c53e481e361e70454f5010c26

Aliases

arxiv: 2605.15052 · arxiv_version: 2605.15052v1 · doi: 10.48550/arxiv.2605.15052 · pith_short_12: 6JWCE2OP4HGM · pith_short_16: 6JWCE2OP4HGMXLNK · pith_short_8: 6JWCE2OP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6JWCE2OP4HGMXLNKAEBT7MP46M \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f26c2269cfe1cccbadaa01033fb1fcf328b8828c53e481e361e70454f5010c26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe630a44129203897421c47415b2db57dc837f98a83cc5a77d3d699e893ed903",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-05-14T16:45:57Z",
    "title_canon_sha256": "505ea8f1ad4ebec84ea99d76a8a40f47f34a86ab610a24b48dc341c91f574491"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15052",
    "kind": "arxiv",
    "version": 1
  }
}