Open Research Index

Eventual categoricity for abstract elementary classes

OpenAI

OpenAI Mathopenai-math/Eventual-Categoricity-for-Abstract-Elementary-ClassesSep 24, 2026math.LOAI-generatedscore 0

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.

SourcePDFJSON

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/openai-math/Eventual-Categoricity-for-Abstract-Elementary-Classes
curl -X POST /api/v1/records/openai-math/Eventual-Categoricity-for-Abstract-Elementary-Classes/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/Eventual-Categoricity-for-Abstract-Elementary-Classes/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'