Split constructions are very widespread in natural languages. The separation of the semantic restriction of a quantifier from that quantifier is a typical example of such a construction. This study addresses the problem that such discontinuous strings exhibit a number of locality constraints, including intervention effects. These are shown to follow from the interaction of a minimalist syntax with a semantics that directly assigns a model-theoretic interpretation to syntactic logical forms. The approach is shown to have wide empirical coverage and a conceptual simplicity. The book will be of interest to scholars and advanced students of syntax and semantics.