On Better-Quasi-Ordering Countable Series-Parallel Orders

  title={On Better-Quasi-Ordering Countable Series-Parallel Orders},
  author={St{\'e}phan Thomass{\'e}},
We prove that any infinite sequence of countable series-parallel orders contains an increasing (with respect to embedding) infinite subsequence. This result generalizes Laver’s and Corominas’ theorems concerning betterquasi-order of the classes of countable chains and trees. Let C be a class of structures and ≤ an order on C. This class is well-quasiordered with respect to ≤ if for any infinite sequence C1, C2, . . . , Ck, . . . in C, there exist i < j such that Ci ≤ Cj . An equivalent… CONTINUE READING