On better-quasi-ordering classes of partial orders

Gregory McKay

Published 2014-08-01, updated 2014-09-09Version 2

We provide a method of constructing better-quasi-orders by generalising a technique for constructing operator algebras that was developed by Pouzet. We then use this method to prove that certain transfinite classes of partial orders are better-quasi-ordered under embeddability. In particular, a class of countable partial orders is better-quasi-ordered whenever the class of indecomposable subsets of its members satisfies a natural strengthening of better-quasi-order. Our main result generalises theorems of Laver, Corominas and Thomass\'e reguarding \sigma-scattered linear orders and trees, countable forests and N-free partial orders respectively.