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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Cofinality changes required for a large set of unapproachable ordinals below $\aleph _{\omega +1}$
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by M. C. Stanley PDF
Proc. Amer. Math. Soc. 135 (2007), 2619-2622 Request permission

Abstract:

In $V$, assume that $\aleph _{\omega }$ is a strong limit cardinal and $2^{\aleph _{\omega }}=\aleph _{\omega +1}$. Let $A$ be the set of approachable ordinals less than $\aleph _{\omega +1}$. An open question of M. Foreman is whether $A$ can be non-stationary in some $\aleph _{\omega }$ and $\aleph _{\omega +1}$ preserving extension of $V$. It is shown here that if $W$ is such an outer model, then ${\{ k<\omega :\text {cf}^{W}(\aleph ^{V}_{k})=\aleph ^{W}_{n} \}}$ is infinite, for each positive integer $n$.
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Additional Information
  • M. C. Stanley
  • Affiliation: Mathematics Department, San Jose State University, San Jose, California 95192
  • Email: stanley@math.sjsu.edu
  • Received by editor(s): December 6, 2005
  • Received by editor(s) in revised form: April 19, 2006, and April 28, 2006
  • Published electronically: February 28, 2007
  • Additional Notes: Research supported by NSF grant DMS-0501114
  • Communicated by: Julia Knight
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2619-2622
  • MSC (2000): Primary 03E05
  • DOI: https://doi.org/10.1090/S0002-9939-07-08760-6
  • MathSciNet review: 2302583