On the cartesian product of well-orderings

TL;DR

This paper calculates the width, an ordinal measure, of well partial orderings formed by the Cartesian product of finitely many well-orderings, advancing understanding of their structural properties.

Contribution

It provides a precise computation of the width for Cartesian products of finitely many well-orderings, a new result in the theory of well partial orderings.

Findings

Computed the width of Cartesian products of finitely many well-orderings

Established a formula for the ordinal rank of the set of antichains

Enhanced understanding of the structure of well partial orderings

Abstract

The width of a well partial ordering (wpo) is the ordinal rank of the set of its antichains ordered by inclusion. We compute the width of wpos obtained as cartesian products of finitely many well-orderings.