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 | References | Similar Articles | Additional Information
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.
- [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] Thomas Jech, On the cofinality of countable products of cardinal numbers, A tribute to Paul Erdős, Cambridge Univ. Press, Cambridge, 1990, pp. 289–305. MR 1117020
- [K] Kenneth Kunen, Elementary embeddings and infinitary combinatorics, J. Symbolic Logic 36 (1971), 407–413. MR 311478, https://doi.org/10.2307/2269948
- [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
