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On well-quasi-ordering lower sets of finite trees

Published online by Cambridge University Press:  24 October 2008

C. St J. A. Nash-Williams
C. St J. A. Nash-Williams
Affiliation:
King's College, Aberdeen
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Abstract

A set Q is quasi-ordered if a reflexive and transitive relation ≤ is defined on Q. It is well-quasi-ordered if it is quasi-ordered and, for every infinite sequence u1, u2,… of elements of Q, there exist i, j such that i < j and ui ≤ uj. A lower set of Q is a subset P of Q such that, if x ≤ y ∈ P, then x ∈ P. The class of lower sets of Q, quasi-ordered by ⊂, is denoted by LQ, and L2Q = L(LQ), etc. The set (, say) of all finite trees is quasi-ordered by writing T1 ≤ T2 if T1 is homeomorphic to a subtree of T2. It is proved that is well-quasi-ordered for all n.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 3 , July 1964 , pp. 369 - 384
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

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