On better quasi-ordering countable trees
In order to obtain a better-quasi-order of the class of countable trees, the author studies ordinal algebras and in particular ordinal algebras associated with trees. Basically, if a (universal) algebra is equipped with a quasi-order such that the operators are increasing and extensive and such that the values increase with the operators, then the resulting algebra is an ordinal algebra. The author derives results for ordinal algebras and for those associated with trees to demonstrate that the class of countable trees is better-quasi-ordered under embeddability. Besides deriving a considerable collection of results, the author is also able to provide a good setting for certain other results, e.g., Pouzet's basis theorem or to make use of results such as the Ramsey-Nash-Williams theorem. In the journey from chains to more complex ordered structures, this paper should prove a valuable addition.
scientific article; zbMATH DE number 3918389