Small forcing creates neither strong nor Woodin cardinals

1998/08/29 by Joel David Hamkins, Hamkins, Joel David, W. Hugh Woodin +1
Computer Science · Mathematics · #03E40 #03E55 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #math.LO #msc:03E40 #msc:03E55

paper · pdf · doi:10.48550/arxiv.math/9808124

6 pages, submitted to the Proceedings of the AMS

arxiv created 1998/08/29 · openalex publication_date 1998/08/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

After small forcing, almost every strongness embedding is the lift of a strongness embedding in the ground model. Consequently, small forcing creates neither strong nor Woodin cardinals.

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