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Proceedings of the American Mathematical Society

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Isomorphisms of trees


Author: Frantisek Franek
Journal: Proc. Amer. Math. Soc. 95 (1985), 95-100
MSC: Primary 04A20; Secondary 03E65
DOI: https://doi.org/10.1090/S0002-9939-1985-0796454-3
MathSciNet review: 796454
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Abstract: Let $ \kappa $, $ \lambda $ be cardinals, $ \kappa \geq {\aleph _1}$ and regular, and $ 2 \leq \lambda \leq \kappa $. If $ \kappa > {\aleph _1}$ and $ \lambda < \kappa $, and if there is a $ \kappa $-Suslin ($ \kappa $-Aronszajn, $ \kappa $-Kurepa) tree, then there are $ {2^\kappa }$ normal $ \lambda $-ary rigid nonisomorphic $ \kappa $-Suslin ($ \kappa $-Aronszajn, $ \kappa $-Kurepa) trees. If there is a Suslin (Aronszajn, Kurepa) tree, then there is a normal rigid Suslin (Aronszajn, Kurepa) tree. If there is a $ \kappa $-Canadian tree, then there are $ {2^\kappa }$ normal $ \lambda $-ary rigid nonisomorphic $ \kappa $-Canadian trees.


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

  • [D] K. J. Devlin and H. Johnsbraten, The Souslin problem, Lecture Notes in Math., vol. 405, Springer-Verlag, Berlin and New York, 1974. MR 0384542 (52:5416)
  • [G] H. Gaifman and E. P. Specker, Isomorphism types of trees, Proc. Amer. Math. Soc. 15 (1964), 1-7. MR 0168484 (29:5746)
  • [F] F. Franek, Some results about saturated ideals and about isomorphisms of $ \kappa $-trees, Ph. D. Thesis, University of Toronto, 1983.
  • [J$ _{1}$] T. J. Jech, Set theory, Academic Press, New York, 1980.
  • [J$ _{2}$] -, Trees, J. Symbolic Logic 36 (1971), 1-14. MR 0284331 (44:1560)
  • [J$ _{3}$] -, Automorphisms of $ {\omega _1}$-trees, Trans. Amer. Math. Soc. 173 (1972), 57-70. MR 0347605 (50:108)
  • [J$ _{4}$] -, Simple complete Boolean algebra, Israel J. Math. 18 (1974). MR 0351812 (50:4300)
  • [T] S. B. Todorcevic, Rigid Aronszajn trees, Publ. Inst. Math. (Beograd) (N. S.) 27 (1980). MR 621958 (82k:04008)

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DOI: https://doi.org/10.1090/S0002-9939-1985-0796454-3
Article copyright: © Copyright 1985 American Mathematical Society

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