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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Regular cardinals in models of $\textrm {ZF}$
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by Moti Gitik PDF
Trans. Amer. Math. Soc. 290 (1985), 41-68 Request permission

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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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 290 (1985), 41-68
  • MSC: Primary 03E35; Secondary 03C62, 03E10
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0787954-5
  • MathSciNet review: 787954