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Article Dans Une Revue Journal of Pure and Applied Algebra Année : 2002

Free $\mu$-lattices

Résumé

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.

Dates et versions

hal-01261049 , version 1 (23-01-2016)

Identifiants

Citer

Luigi Santocanale. Free $\mu$-lattices. Journal of Pure and Applied Algebra, 2002, Category Theory 1999: selected papers, conference held in Coimbra in honour of the 90th birthday of Saunders Mac Lane, 168 (2--3), pp.227-264. ⟨10.1016/S0022-4049(01)00098-6⟩. ⟨hal-01261049⟩
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