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Diamonds, uniformization

  • Saharon Shelah (a1) (a2)

Abstract

Assume G.C.H. We prove that for singular λ, □λ implies the diamonds hold for many S ⊆ λ+ (including S ⊆ {δ:δ ∈ λ+, cf δ = cf λ}.) We also have complementary consistency results.

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References

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[DS]Devlin, K. and Shelah, S., A weak form of the diamond which follows from 20 < 21, Israel Journal of Mathematics, vol. 29 (1978), pp. 239247.
[DJ]Devlin, K. and Johnsbråten, H., The Souslin problem, Lecture Notes in Mathematics, vol. 405, Springer-Verlag, Berlin, 1974.
[Gr]Gregory, J., Higher Souslin trees, this Journal, vol. 41 (1976), pp. 663671.
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[K]Keisler, H. J., Models with tree structures, Proceedings of the Tarski Symposium (Berkeley, 1971; Henkin, L., editor), Proceedings of Symposia in Pure Mathematics, vol. 25, American Mathematical Society, Providence, R.I., 1974, pp. 331348.
[Sh1]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin, 1982.
[Sh2]Shelah, S., Whitehead groups may not be free even assuming CH. I, Israel Journal of Mathematics, vol. 28 (1977), pp. 193203.
[Sh3]Shelah, S., On successors of singular cardinals, Logic Colloquium '78 (Boffa, M., van Dalen, D. and McAloon, K., editors), Studies in Logic and the Foundations of Mathematics, vol. 97, North-Holland, Amsterdam. 1979, pp. 357380.
[Sh4]Shelah, S., Whitehead groups may not be free even assuming CH. II, Israel Journal of Mathematics, vol. 35 (1980), pp. 257285.
[SK]Steinhorn, C.J. and King, J. H., The uniformization property for ℵ2, Israel Journal of Mathematics, vol. 36 (1980), pp. 248256.
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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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