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Regular cardinals in models of $ {\rm ZF}$


Author: Moti Gitik
Journal: Trans. Amer. Math. Soc. 290 (1985), 41-68
MSC: Primary 03E35; Secondary 03C62, 03E10
MathSciNet review: 787954
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Abstract: We prove the following

Theorem. Suppose $ M$ is a countable model of $ ZFC$ and $ \kappa $ is an almost huge cardinal in $ M$. Let $ A$ be a subset of $ \kappa $ consisting of nonlimit ordinals. Then there is a model $ {N_A}$ of $ ZF$ such that $ {\aleph _\alpha }$ is a regular cardinal in $ {N_A}$ iff $ \alpha \in A$ for every $ \alpha > 0$.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0787954-5
Article copyright: © Copyright 1985 American Mathematical Society