The Alternation Hierarchy for the Theory of -lattices

The alternation hierarchy problem asks whether every $\mu$ -term, that is a term built up using also a least fixed point constructor as well as a greatest fixed point constructor, is equivalent to a $\mu$ -term where the number of nested fixed point of a different type is bounded by a fixed number.

In this paper we give a proof that the alternation hierarchy for the theory of $\mu$ -lattices is strict, meaning that such number does not exist if $\mu$ -terms are built up from the basic lattice operations and are interpreted as expected. The proof relies on the explicit characterization of free $\mu$ -lattices by means of games and strategies

Abstract: