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We provide a characterization theorem, in the style of van Ben them and Janin-Walukiewicz, for the alternation-free fragment of the modal mu-calculus. For this purpose we introduce a variant of standard monadic second-order logic (MSO), which we call well-founded monadic second-order logic (WFMSO). When interpreted in a tree model, the second-order quantifiers of WFMSO range over subsets of conversely...
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