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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Small forcing creates neither strong nor Woodin cardinals
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by Joel David Hamkins and W. Hugh Woodin
Proc. Amer. Math. Soc. 128 (2000), 3025-3029
DOI: https://doi.org/10.1090/S0002-9939-00-05347-8
Published electronically: April 28, 2000

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.
References
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Bibliographic Information
  • Joel David Hamkins
  • Affiliation: Mathematics Program, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, New York 10016
  • MR Author ID: 347679
  • Email: jhamkins@gc.cuny.edu
  • W. Hugh Woodin
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
  • Email: woodin@math.berkeley.edu
  • Received by editor(s): September 1, 1998
  • Received by editor(s) in revised form: November 9, 1998
  • Published electronically: April 28, 2000
  • Additional Notes: The research of the first author has been supported in part by grants from the PSC-CUNY Research Foundation, and of the second author, by grants from the NSF
  • Communicated by: Carl G. Jockusch, Jr.
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 3025-3029
  • MSC (1991): Primary 03E55, 03E40
  • DOI: https://doi.org/10.1090/S0002-9939-00-05347-8
  • MathSciNet review: 1664390