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Souslin trees which are hard to specialise

Author: James Cummings
Journal: Proc. Amer. Math. Soc. 125 (1997), 2435-2441
MSC (1991): Primary 03E05; Secondary 03E35
MathSciNet review: 1376756
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Abstract: We construct some $\kappa ^+$-Souslin trees which cannot be specialised by any forcing which preserves cardinals and cofinalities. For $\kappa $ a regular cardinal we use the $ \begin {picture}(6,6)(0,0) \drawline (0,3)(3,6)(6,3) (3,0)(0,3) \drawline (0,6)(6,6)(6,0) (0,0)(0,6) \end {picture} $ principle, and for $\kappa $ singular we use squares and diamonds.

References [Enhancements On Off] (What's this?)

  • 1. J. Baumgartner, J. Malitz and W. Reinhardt, Embedding trees in the rationals, Proceedings of the National Academy of Sciences 67 (1970), pp 1748-1753. MR 47:3172
  • 2. K. J. Devlin, Reduced products of $\aleph _2$-trees, Fundamenta Mathematicae 118 (1983), pp 129-134. MR 85i:03156
  • 3. C. Gray, Iterated forcing from the strategic point of view, PhD thesis, University of California, Berkeley, 1980.
  • 4. A. Levy, Basic set theory, Springer-Verlag, Berlin, 1979. MR 80k:04001
  • 5. S. Shelah, On successors of singular cardinals, in Logic Colloquium '78 (ed: M. Boffa, D. van Dalen and K. McAloon), North-Holland, Amsterdam, pp 357-380. MR 82d:03079
  • 6. S. Shelah and L. Stanley, Weakly compact cardinals and non-special Aronszajn trees, Proceedings of the American Mathematical Society 104 (1988), pp 887-897. MR 90e:03060

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Additional Information

James Cummings
Affiliation: Mathematics Institute, Hebrew University, Givat Ram, 91904 Jerusalem, Israel
Address at time of publication: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890

Keywords: Souslin trees, ascent paths, squares and diamonds
Received by editor(s): September 7, 1995
Received by editor(s) in revised form: February 12, 1996
Additional Notes: The author was supported by a Postdoctoral Fellowship at the Mathematics Institute, Hebrew University of Jerusalem
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society

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