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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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.


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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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