We characterize those formulas of MSO m(monadic second-order logic) that are safe for bisimulation: formulas defining binary relations such that any bisimulation is also a bisimulation with\ud respect to these defined relations. Every such formula is equivalent to one constructed from μ-calculus tests, atomic actions and the regular operations. The proof uses a characterization of\ud completely additive μ-calculus formulas: formulas ø(p) that distribute over arbitrary unions. It\ud turns out that complete additivity is equivalent to distributivity over countable unions.\ud For FOL (first-order logic) a similar theorem is shown (giving an alternative proof to the original of ). Here though distributivity over finite unions is sufficient. This enables us to show\ud that the characterization of safe FOL-formulas carries over to the setting of finite models
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