Geodesic
The alternation hierarchy for the theory of μ-lattices
Theory and applications of categories, CT2000, Tome 9 (2000), pp. 166-197.

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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.
Classification : 03D55, 06B25, 91A43.
Mots-clés : free lattices, free �-lattices, fixed points, parity games. 
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     author = {Luigi Santocanale},
     title = {The alternation hierarchy for the theory of $\mu$-lattices},
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     pages = {166--197},
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     volume = {9},
     year = {2000},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/TAC_2000__9_a8/}
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Luigi Santocanale. The alternation hierarchy for the theory of $\mu$-lattices. Theory and applications of categories, CT2000, Tome 9 (2000), pp. 166-197. https://geodesic-test.mathdoc.fr/item/TAC_2000__9_a8/