The reverse mathematics of wqos and bqos

TL;DR

This paper surveys the reverse mathematics of well-quasi-orderings and better-quasi-orderings, analyzing foundational results, classification challenges, and recent progress on open problems in the field.

Contribution

It provides a comprehensive classification of wqo and bqo results within reverse mathematics, including elementary and advanced theorems, and discusses recent developments on longstanding open problems.

Findings

Classification of wqo and bqo results in reverse mathematics

Equivalence of different definitions and basic closure properties

Progress on long-standing open problems

Abstract

In this paper we survey wqo and bqo theory from the reverse mathematics perspective. We consider both elementary results (such as the equivalence of different definitions of the concepts, and basic closure properties) and more advanced theorems. The classification from the reverse mathematics viewpoint of both kinds of results provides interesting challenges, and we cover also recent advances on some long standing open problems.