The Alternation Hierarchy for the Theory of Μ-lattices
نویسنده
چکیده
The alternation hierarchy problem asks whether every μ-term φ, that is, a term built up also using a least fixed point constructor as well as a greatest fixed point constructor, is equivalent to a μ-term where the number of nested fixed points of a different type is bounded by a constant independent of φ. In this paper we give a proof that the alternation hierarchy for the theory of μ-lattices is strict, meaning that such a constant does not exist if μ-terms are built up from the basic lattice operations and are interpreted as expected. The proof relies on the explicit characterization of free μ-lattices by means of games and strategies.
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