Open Research Index

A counterexample to Vaught's conjecture for infinitary logic

Nathanael Ackerman, Cameron Freer, Robin Knight

Palomar Registrypalomar/PALOMAR-2026-10-07-000001Oct 7, 2026math.LOscore 0

There is a counterexample to Vaught's conjecture for L_{omega_1,omega}. This formalization is based on an unpublished draft by Robin Knight. It constructs a sentence in a countable relational language with exactly aleph-one isomorphism classes of countable models and no nonempty perfect set of pairwise nonisomorphic model codes. This is not a counterexample to the first-order Vaught conjecture.

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-2026-10-07-000001
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-07-000001/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-07-000001/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'