2023/03/20 by Abraham, Uri, Bonnet, Robert, Džamonja, Mirna +1
#FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.2303.11451
The following is a 2008 conjecture of Abraham, Bonnet and Kubiś: [ABK Conjecture] Every well quasi order (wqo) is a countable union of better quasi orders (bqo). We obtain a partial progress on the conjecture, by showing that the class of orders that are a countable union of better quasi orders (sigma-bqo) is closed under various operations. These include diverse products, such as the Dress-Shieffels product. We develop various properties of the latter product. In relation with the main question, we explore the class of alpha-wqo for countable ordinals alpha and obtain several closure properties and a Hausdorff-style classification theorem. Our main contribution is the discovery of various properties of sigma-bqos and ruling out potential counterexamples to the ABK Conjecture.