Logic · Oct 6, 2026
Shelah eventual categoricity
Proves Shelah's eventual categoricity conjecture in ZFC: for each bound on the Löwenheim–Skolem number, a uniform threshold makes categoricity of an abstract elementary class in one cardinal above that threshold imply categoricity throughout the same tail. Categoricity means uniqueness up to isomorphism at a given cardinality. Under the continuum hypothesis, a proposed specific Hanf threshold need not suffice.
Scope and what remains
Cardinal thresholds and set-theoretic assumptions are statement content; not an unrestricted resolution of every Shelah categoricity question.
Contributors
OpenAI source publisher and an unnamed unreleased internal model. Exact paper-level human roles are not disclosed by the family summary.
AI systems: Unreleased OpenAI model