{"id":"openai-math/Eventual-Categoricity-for-Abstract-Elementary-Classes","pdf":"https://github.com/openai/math/blob/main/preprints/Eventual-Categoricity-for-Abstract-Elementary-Classes-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Eventual-Categoricity-for-Abstract-Elementary-Classes-September-24-2026","tags":["model-theory","abstract-elementary-classes","set-theory"],"score":0,"title":"Eventual categoricity for abstract elementary classes","domain":"Mathematical logic","family":"240","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.LO","summary":"We prove Shelah's eventual categoricity conjecture for abstract elementary classes in ZFC. For each infinite bound on the Löwenheim–Skolem number there is a uniform threshold such that categoricity in any one cardinal at or above that threshold implies categoricity in every cardinal at or above the same threshold.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Shelah's eventual categoricity and the prescribed-threshold obstruction"}