Abstract
The closure ordinal of a µ -calculus formula ϕ(x) is the least ordinal α, if it exists, such that, in any model, the least fixed point of ϕ(x) can be computed in at most α many steps, by iteration of the meaning function associated with ϕ(x), starting from the empty set. In this paper we focus on closure ordinals of the two-way modal µ -calculus. Our main technical contribution is the construction of a two-way formula ϕn with closure ordinal ωn for an arbitrary nЄω. Building on this construction, as our main result we define a two-way formula ϕα with closure ordinal α for an arbitrary α
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Milanese, G. C., & Venema, Y. (2019). Closure Ordinals of the Two-Way Modal µ -Calculus. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11541 LNCS, pp. 498–515). Springer Verlag. https://doi.org/10.1007/978-3-662-59533-6_30
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