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This paper is concerned with generalization issues for a decision tree learner for structured data called Alkemy. Motivated by error bounds established in statistical learning theory, we study the VC dimensions of some predicate classes defined on sets and multisets – two data-modelling constructs used intensively in the knowledge representation formalism of Alkemy – and from that obtain insights into the (worst-case) generalization behaviour of the learner. The VC dimension results and the techniques used to derive them may be of wider independent interest.