2021/12/19 by Sittinon Jirattikansakul, Jirattikansakul, Sittinon
Mathematics · #03E04 #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2112.10261
openalex publication_date 2021/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We build a supercompact version of the forcing defined in \citegitik2019. For each singular cardinal in the ground model with any fixed cofinality, which is a limit of supercompact cardinals, it is possible to force so that the size of the powerset of the singular cardinal is arbitrarily large, while preserving the singular cardinal. An important feature of this forcing is that it is possible to define the forcing so that the successor of the singular cardinal is collapsed, but all the cardinals above it are preserved.