 By “externally classified”, Hooker refers to the sort of cross-classification that holds across different determinable/determinate hierarchies. To address some self-assessed shortcomings of Hooker’s own formulation of his general account of reduction, Bickle (1998) reformulates Hooker’s insights, including his token-token reduction supplement, within a set-theoretically characterized “semantic” account of theory structure and relations. Bickle’s account draws directly on formal work from “structuralist” philosophy of science. More recently Klein (2013) advocated for a semantic “sets of models” account of theory structure as a strategy for accommodating multiple realized reduced kinds.