2021/02/18 by Brent Cody, Cody, Brent
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2102.09591
openalex publication_date 2021/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Building on work of Holy, Lücke and Njegomir \citeMR3913154 on small embedding characterizations of large cardinals, we use some classical results of Baumgartner (see \citeMR0384553 and \citeMR0540770), to give characterizations of several well-known large cardinal ideals, including the Ramsey ideal, in terms of generic elementary embeddings; we also point out some seemingly inherent differences between small embedding and generic embedding characterizations of subtle cardinals. Additionally, we present a simple and uniform proof which shows that, when κ is weakly compact, many large cardinal ideals on κ are nowhere κ-saturated. Lastly, we survey some recent consistency results concerning the weakly compact ideal as well as some recent results on the subtle, ineffable and Π11-indescribable ideals on Pκλ, and we close with a list of open questions.