Hostname: page-component-6898cfcb55-cbk24 Total loading time: 0 Render date: 2026-11-11T05:41:57.546Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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

Information

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