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REFLECTION OF STATIONARY SETS AND THE TREE PROPERTY AT THE SUCCESSOR OF A SINGULAR CARDINAL

  • LAURA FONTANELLA (a1) and MENACHEM MAGIDOR (a2)

Abstract

We show that from infinitely many supercompact cardinals one can force a model of ZFC where both the tree property and the stationary reflection hold at א ω 2+1.

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References

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[1] Eklof, P., On the existence of κ free Abelian groups . Proceedings of the American Mathematical Society, vol. 47 (1975), pp. 6572.
[2] Kunen, K., Saturated ideals, this Journal, vol. 43 (1978), no. 1, pp. 6576.
[3] Laver, R., Making the supercompactness of κ indestructible under κ-directed closed forcing . Israel Journal of Mathematics, vol. 29 (1978), pp. 385388.
[4] Magidor, M. and Shelah, S., The tree property at successors of singular cardinals . Archive for Mathematical Logic, vol. 35 (1996), no. 5–6, pp. 385404.
[5] Magidor, M. and Shelah, S., When does almost free imply free? (For groups, transversals, etc.). Journal of the American Mathematical Society, vol. 7 (1994), no. 4, pp. 769830.
[6] Mitchell, W. J., Aronszajn trees and the independence of the transfer property . Annals of Mathematical Logic, vol. 5 (1972), pp. 2146.
[7] Neeman, I., The tree property up to א ω+1, this Journal, vol. 79 (2014), pp. 429459.
[8] Shelah, S., A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals . Israel Journal of Mathematics, vol. 21 (1975), pp. 319339.
[9] Shelah, S., On successors of singular cardinals . Logic Colloquium (Boffa, M., Van Dallen, D., and McAloon, K., editors), Studies in Logic and the Foundations of Mathematics, vol. 78, North Holland, Amsterdam, 1979, pp. 357380.
[10] Sinapova, D., The tree property at א ω+1, this Journal, vol. 77 (2012), no. 1, pp. 279290.
[11] Unger, S., Fragility and indestructibility of the tree property . Archive for Mathematical Logic, vol. 51 (2012), no. 5–6, pp. 635645.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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