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The consistency strength of successive cardinals with the tree property

  • Matthew Foreman (a1), Menachem Magidor (a2) and Ralf-Dieter Schindler (a3) (a4)

Abstract.

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

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References

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[1]Abraham, U., Aronszajn trees on ℵ2 and ℵ3, Annals of Pure and Applied Logic, vol. 24 (1983), pp. 213230.
[2]Cummings, J. and Foreman, M., The tree property, preprint.
[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.
[4]Jech, T., Set theory, San Diego, 1978.
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[6]Mitchell, W., Aronszajn trees and the independence of the transfer property, Annals of Mathematical Logic, vol. 5 (1972), pp. 2146.
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[9]Neeman, I., Optimal proofs of determinacy, The Bulletin of Symbolic Logic, vol. 1 (1995), pp. 327339.
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[11]Schimmerling, E. and Steel, J. R., The maximality of the core model, Transactions of the American Mathematical Society, to appear.
[12]Schimmerling, E. and Woodin, H., The Jensen covering property, to appear.
[13]Schindler, R.-D., The core model up to one strong cardinal, Ph.D. thesis, Bonner Mathematische Schriften, Bonn, 1996.
[14]Schindler, R.-D., Successive weakly compact or singular cardinals, this Journal, vol. 64 (1999), pp. 139146.
[15]Schindler, R.-D., Weak covering and the tree property, Archive of Mathematical Logic, vol. 38 (1999), pp. 515520.
[16]Schindler, R.-D. and Steel, J. R., The strength of AD, preprint.
[17]Steel, J. R., Projectively well-ordered inner models, Annals of Pure and Applied Logic, vol. 74 (1995), pp. 77104.
[18]Steel, J. R., The core model iterability problem, Berlin, 1996.

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