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We characterize the expressive power of the modal mu-calculus on monotoneneighborhood structures, in the style of the Janin-Walukiewicz theorem for thestandard modal mu-calculus. For this purpose we consider a monadic second-orderlogic for monotone neighborhood structures. Our main result shows that themonotone modal mu-calculus corresponds exactly to the fragment of thissecond-order language that is invariant for neighborhood bisimulations.

Expressiveness of the modal mu-calculus on monotone neighborhood structures