Author:
Nash-Williams C. St J. A.
Abstract
AbstractA 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.
Publisher
Cambridge University Press (CUP)
Reference4 articles.
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3. On well-quasi-ordering finite trees
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