Free -lattices

A $\mu$ -lattice is a lattice with the property that every unary polynomial has both a least and a greatest fix-point. In this paper we define the quasivariety of $\mu$ -lattices and, for a given partially ordered set

, we construct a $\mu$ -lattice ${\cal J}_{P}$ whose elements are equivalence classes of games in a preordered class ${\cal J}(P)$ . We prove that the $\mu$ -lattice ${\cal J}_{P}$ is free over the ordered set

and that the order relation of $\mathcal{J}_{P}$ is decidable if the order relation of

is decidable. By means of this characterization of free $\mu$ -lattices we infer that the class of complete lattices generates the quasivariety of $\mu$ -lattices

Abstract: