On Well-Quasi-Ordering Finite Trees

  • C. ST. J. A. Nash-Williams
Part of the Modern Birkhäuser Classics book series (MBC)


A new and simple proof is given of the known theorem that, if T 1 , T 2, … , is an infinite sequence of finite trees, then there exist i and j such that i < j and T i is homeomorphic to a subtree of T j.


Simple Proof Research Note Infinite Sequence Cardinal Number Cartesian Product Versus 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (1).
    Higman. G. Ordering by divisibility in abstract algebras. Proc. London Math. Soc. (3), 2 (1952), 326–336.Google Scholar
  2. (2).
    Kruskal,. J. B. Well-quasi-ordering, the tree theorem, and Vázsony’s conjecture. Trans. American Math. Soc. 95 (1960). 210–225.MATHMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • C. ST. J. A. Nash-Williams
    • 1
  1. 1.King’s CollegeAberdeenUSA

Personalised recommendations