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A new proof of Kunen's inconsistency


Author: Jindrich Zapletal
Journal: Proc. Amer. Math. Soc. 124 (1996), 2203-2204
MSC (1991): Primary 03E55
DOI: https://doi.org/10.1090/S0002-9939-96-03281-9
MathSciNet review: 1317054
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Abstract: Using a basic fact from Shelah's theory of possible cofinalities, we give a new proof of Kunen's inconsistency theorem: there is no nontrivial elementary embedding of the set-theoretical universe into itself.


References [Enhancements On Off] (What's this?)

  • [B] D. Burke, Splitting stationary sets, preprint.
  • [H] M. Harada, Another proof for Kunen's theorem, preprint.
  • [J1] T. Jech, Set Theory, Academic Press, New York, 1978.
  • [J2] T. Jech, On the cofinality of countable products of cardinal numbers, A Tribute to P. Erdos (A. Baker, N. Bollobás and A. Hajnal, eds.), Cambridge University Press, Cambridge, 1990, pp. 289--306. MR 92m:03083
  • [K] K. Kunen, Elementary embeddings and infinitary combinatorics, J. Symbolic Logic 36 (1971), 407--413. MR 47:40
  • [S] S. Shelah, Cardinal arithmetic, Oxford Logic Guides, vol. 29, Clarendon Press, Oxford, 1994.

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Additional Information

Jindrich Zapletal
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Address at time of publication: M.S.R.I., 1000 Centennial Dr., Berkeley, California 94720
Email: jindra@msri.org

DOI: https://doi.org/10.1090/S0002-9939-96-03281-9
Received by editor(s): November 14, 1994
Received by editor(s) in revised form: January 20, 1995
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1996 American Mathematical Society

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