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We prove a general decomposition theorem for the modal μ-calculus L_μ in the spirit of Feferman and Vaught's theorem for disjoint unions. In particular, we show that if a structure (i.e., transition system) is composed of two substructures M_1 and M_2 plus edges from M_1 to M_2, then the formulas true at a node in M only depend on the formulas true in the respective substructures in a sense made precise below. As a consequence we show that the model-checking problem for L_μ is fixed-parameterdoi:10.1145/2603088.2603144 dblp:conf/csl/BojanczykDK14 fatcat:vfhrvywtezbvjis7i3mglnqzfq