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Tree self-embeddings

Published online by Cambridge University Press:  20 November 2018

David Ross
David Ross*
Affiliation:
Department of Pure Mathematics, University of Hull, Hull, HU6 7RX, England
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Abstract

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Elementary proofs are given of the following two statements: (1) Every infinite tree of height at most ω properly embeds into itself. (2) There is a tree of height ω + 1 that does not properly embed into itself.

Keywords

02K0402K06
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 1 , 01 March 1989 , pp. 30 - 33
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Jech, T., Set theory, Academic Press (New York) 1978.Google Scholar
2. Laver, R., Better-quasi-orderings and a class of trees, Studies in Foundations and Combinatorics, Advances in Mathematics Supplementary Studies, Vol. 1, Academic Press (New York) (1978), pp. 31–48.Google Scholar
3. St, C.. J. A. Nash-Williams, On well-quasi-ordering infinite trees, Proc. Camb. Phil. Soc. 61 (1965), pp. 697–720. Google Scholar
4. , On better-quasi-ordering transfinite sequences, Proc. Camb. Phil. Soc. 64 (1968), pp. 273–290. Google Scholar
5. Kruskal, J. B., Well quasi-ordering, the tree theorem, and Vazsony's conjecture, Trans. Amer. Math. Soc. 95 (1960), pp. 210–225. Google Scholar