Violating the Singular Cardinals Hypothesis Without Large Cardinals

2011/07/08 by Moti Gitik, Peter Koepke, Gitik, Moti +1
Computer Science · Mathematics · #03E25 #03E35 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1107.1667

openalex publication_date 2011/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend a transitive model V of ZFC + GCH cardinal preservingly to a model N of ZF + "GCH holds below Alef_omega" + "there is a surjection from the power set of Alef_omega onto lambda" where lambda is an arbitrarily high fixed cardinal in V.

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