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A new proof of Kunen's inconsistency
Author(s):
Jindrich
Zapletal
Journal:
Proc. Amer. Math. Soc.
124
(1996),
2203-2204.
MSC (1991):
Primary 03E55
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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:
- [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:
10.1090/S0002-9939-96-03281-9
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
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