{"id":"palomar/PALOMAR-2026-10-07-000001","url":"https://github.com/cameronfreer/vaught-conjecture-palomar/tree/032ccb7a25b0ff6227128aa0aeba549c5901ea9a","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-07-000001-v1.json","repo":"https://github.com/cameronfreer/vaught-conjecture-palomar","tags":["math.LO","msc:03C15","msc:03C75","msc:03E15","model-theory","infinitary-logic","vaught-conjecture","lean-formalization"],"score":0,"title":"A counterexample to Vaught's conjecture for infinitary logic","trust":"high","domain":"math.LO","source":"palomar","authors":["Nathanael Ackerman","Cameron Freer","Robin Knight"],"reviews":0,"subject":"math.LO","summary":"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 This formalization is based on an unpublished draft by Robin Knight.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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-07","reactions":{},"formalized":true,"formalizes":[{"title":"Unpublished draft on a counterexample to infinitary Vaught's conjecture","identifier":"","relationship":"formalizes"}]}