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.