2024/01/05 by Asaf Karagila, Karagila, Asaf, Jiachen Yuan +1
Mathematics · #03E25 #03E35 (Secondary) #03E55 (Primary) #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO #msc:03E25 #msc:03E35 #msc:03E55
paper · pdf · doi:10.48550/arxiv.2401.02951
8 pages; final version
openalex publication_date 2024/01/05 · openalex created_date 2025/10/10 · arxiv created 2026/07/30 · arxiv updated 2026/07/31 · openalex updated_date 2026/08/01
Hayut and the first author isolated the notion of a critical cardinal in [1]. In this work, we answer several questions raised in the original paper. We show that it is consistent for a critical cardinal not to have any ultrapower elementary embeddings, as well as that it is consistent that no target model is closed. We also prove that if κ is a critical point by any ultrapower embedding, then it is the critical point of an ultrapower embedding by a normal measure. The paper concludes by presenting several open questions of interest in the study of critical cardinals.