Lean formalization in OpenAI math repository (Result 240)
Model / AI: OpenAI (unreleased)
OpenAI's internal frontier model proved and formalized in Lean the main result of 'A CH obstruction to a prescribed categoricity threshold'. Assuming the continuum hypothesis, we construct an abstract elementary class with Löwenheim–Skolem number ℵ0 that is categorical in every sufficiently large cardinal but has at least two nonisomorphic models of cardinality \beth_{\omega_2}. Thus categoricity does not transfer down to the proposed bound \beth_{(2^{\aleph_0})^+}, which equals \beth_{\omega_2} under CH. Consequently, if ZFC is consistent, the prescribed-threshold form of Shelah's categoricity conjecture is not provable in ZFC.
Source read 2026-10-08. Cataloged from OpenAI's formalization.yaml (Family 240). The Lean development was not rebuilt locally.