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The consistency strength of successive cardinals with the tree property

Published online by Cambridge University Press:  12 March 2014

Matthew Foreman ,
Menachem Magidor  and
Ralf-Dieter Schindler
Matthew Foreman
Affiliation:
Department of Mathematics, University of California at Irvine, Irvine, California 92697, USA, E-Mail: mforeman@math.uci.edu
Menachem Magidor
Affiliation:
Institue of Mathematics, Hebrew University, Jerusalem 91904, Israel, E-Mail: menachem@math.huji.ac.il
Ralf-Dieter Schindler
Affiliation:
Department of Mathematics, University of California at Berkeley, Berkeley California 94720, USA Institut Für Formale Logik, Universitaet Wien, 1090 Wien, Austria, E-Mail: rds@logic.univie.ac.at
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Abstract.

If ωn has the tree property for all 2 ≤ n < ω and , then for all and n < ω. Mnt(X) exists.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 4 , December 2001 , pp. 1837 - 1847
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

[1]Abraham, U., Aronszajn trees on ℵ2 and ℵ3, Annals of Pure and Applied Logic, vol. 24 (1983), pp. 213–230.CrossRefGoogle Scholar
[2]Cummings, J. and Foreman, M., The tree property, preprint.Google Scholar
[3]Devlin, K. and Jensen, R. B., Marginalia to a theorem of Silver, Logic conference Kiel 1974, Lecture Notes in Mathematics, vol. 499, Springer-Verlag, Berlin, p. 976.Google Scholar
[4]Jech, T., Set theory, San Diego, 1978.Google Scholar
[5]Jensen, R. B., The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229–308.CrossRefGoogle Scholar
[6]Mitchell, W., Aronszajn trees and the independence of the transfer property, Annals of Mathematical Logic, vol. 5 (1972), pp. 21–46.CrossRefGoogle Scholar
[7]Mitchell, W. and Schimmerling, E., Covering without countable closure, Mathematical Research Letters, vol. 2 (1995), pp. 595–609.CrossRefGoogle Scholar
[8]Mitchell, W. and Steel, J. R., Fine structure and iteration trees, Berlin, 1994.CrossRefGoogle Scholar
[9]Neeman, I., Optimal proofs of determinacy, The Bulletin of Symbolic Logic, vol. 1 (1995), pp. 327–339.CrossRefGoogle Scholar
[10]Schimmerling, E., A finite family weak square principle, this Journal, vol. 64 (1999), pp. 1087–1110.Google Scholar
[11]Schimmerling, E. and Steel, J. R., The maximality of the core model, Transactions of the American Mathematical Society, to appear.Google Scholar
[12]Schimmerling, E. and Woodin, H., The Jensen covering property, to appear.Google Scholar
[13]Schindler, R.-D., The core model up to one strong cardinal, Ph.D. thesis, Bonner Mathematische Schriften, Bonn, 1996.Google Scholar
[14]Schindler, R.-D., Successive weakly compact or singular cardinals, this Journal, vol. 64 (1999), pp. 139–146.Google Scholar
[15]Schindler, R.-D., Weak covering and the tree property, Archive of Mathematical Logic, vol. 38 (1999), pp. 515–520.CrossRefGoogle Scholar
[16]Schindler, R.-D. and Steel, J. R., The strength of AD, preprint.Google Scholar
[17]Steel, J. R., Projectively well-ordered inner models, Annals of Pure and Applied Logic, vol. 74 (1995), pp. 77–104.CrossRefGoogle Scholar
[18]Steel, J. R., The core model iterability problem, Berlin, 1996.CrossRefGoogle Scholar