Open Research Index

elliotglazer/erdos501

Elliot Glazer

Palomar Registrypalomar/PALOMAR-2026-08-19-000002Sep 6, 2026math.LOscore 0

Erdős problem #501 (Erdős 1961; Erdős–Hajnal 1971, Problem 38): for every real x let A_x be a bounded set of reals of Lebesgue outer measure < 1; must there be an infinite independent set, i.e. an infinite X ⊆ ℝ with x ∉ A_y for all distinct x, y ∈ X? And if the sets A_x are closed of measure < 1, must there be an independent set of size 3? This repository formalizes both answers. Second question: yes — closed sets of measure < 1 admit an infinite independent set (Newelski–Pawlikowski–Seredyński 1987; no boundedness is needed), hence one of size 3. First question: independent of ZFC. Under…

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-08-19-000002
curl -X POST /api/v1/records/palomar/PALOMAR-2026-08-19-000002/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-08-19-000002/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'