A new proof of Kunen’s inconsistency
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- by Jindrich Zapletal PDF
- Proc. Amer. Math. Soc. 124 (1996), 2203-2204 Request permission
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
- D. Burke, Splitting stationary sets, preprint.
- M. Harada, Another proof for Kunen’s theorem, preprint.
- T. Jech, Set Theory, Academic Press, New York, 1978.
- 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
- Kenneth Kunen, Elementary embeddings and infinitary combinatorics, J. Symbolic Logic 36 (1971), 407–413. MR 311478, DOI 10.2307/2269948
- S. Shelah, Cardinal arithmetic, Oxford Logic Guides, vol. 29, Clarendon Press, Oxford, 1994.
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
- Received by editor(s): November 14, 1994
- Received by editor(s) in revised form: January 20, 1995
- Communicated by: Andreas R. Blass
- © Copyright 1996 American Mathematical Society
- 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