The ABK Conjecture on countable unions of bqos
A well-quasi-order (wqo) is a quasi-order with no infinite descending sequence and no infinite antichain; a better-quasi-order (bqo) is a wqo satisfying the stronger Ramsey-theoretic condition recalled in the source. A countable union of bqos means a wqo whose underlying set is the union of countably many subsets, each carrying a bqo induced by the quasi-order. ABK Conjecture. Every wqo is a countable union of bqo.
References
Primary source
Uri Abraham, Robert Bonnet, Mirna Džamonja and Maurice Pouzet, “On the ABK Conjecture, alpha-well Quasi Orders and Dress-Schiffels product”, arXiv:2303.11451 (2025).
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