A μ-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 μ-lattices and, for a given partially ordered set P, we construct a μ-lattice JP whose elements are equivalence classes of games in a preordered class J(P). We prove that the μ-lattice JP is free over the ordered set P and that the order relation of JP is decidable if the order relation of P is decidable. By means of this characterization of free μ-lattices we infer that the class of complete lattices generates the quasivariety of μ-lattices.
Journal of Pure and Applied Algebra, 2002, Vol 168, Issue 2-3, p. 227-264
μ-lattice; greatest fix-point; quasivariety of μ-lattices