1.  19
    Luca Alberucci & Alessandro Facchini (2009). The Modal Μ-Calculus Hierarchy Over Restricted Classes of Transition Systems. Journal of Symbolic Logic 74 (4):1367 - 1400.
    We study the strictness of the modal μ-calculus hierarchy over some restricted classes of transition systems. First, we prove that over transitive systems the hierarchy collapses to the alternationfree fragment. In order to do this the finite model theorem for transitive transition systems is proved. Further, we verify that if symmetry is added to transitivity the hierarchy collapses to the purely modal fragment. Finally, we show that the hierarchy is strict over reflexive frames. By proving the finite model theorem for (...)
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  2.  39
    Luca Alberucci & Alessandro Facchini (2009). On Modal Μ -Calculus and Gödel-Löb Logic. Studia Logica 91 (2):145 - 169.
    We show that the modal µ-calculus over GL collapses to the modal fragment by showing that the fixpoint formula is reached after two iterations and answer to a question posed by van Benthem in [4]. Further, we introduce the modal µ~-calculus by allowing fixpoint constructors for any formula where the fixpoint variable appears guarded but not necessarily positive and show that this calculus over GL collapses to the modal fragment, too. The latter result allows us a new proof of the (...)
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  3.  2
    Luca Alberucci & Alessandro Facchini (2009). On Modal Μ-Calculus and Gödel-Löb Logic. Studia Logica 91 (2):145-169.
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