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Free μ-lattices

✍ Scribed by Luigi Santocanale

Book ID
104152466
Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
288 KB
Volume
168
Category
Article
ISSN
0022-4049

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✦ Synopsis

A -lattice is a lattice with the property that every unary polynomial has both a least and a greatest ÿx-point. In this paper we deÿne the quasivariety of -lattices and, for a given partially ordered set P, we construct a -lattice J P whose elements are equivalence classes of games in a preordered class J(P). We prove that the -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 -lattices we infer that the class of complete lattices generates the quasivariety of -lattices.

📜 SIMILAR VOLUMES

Free compact lattices
Free compact lattices
✍ S. A. Liber 📂 Article 📅 1978 🏛 SP MAIK Nauka/Interperiodica 🌐 English ⚖ 249 KB
Singular covers in free lattices
Singular covers in free lattices
✍ Ralph Freese; J. B. Nation; J. Ježek; V. Slavík 📂 Article 📅 1986 🏛 Springer Netherlands 🌐 English ⚖ 428 KB

A covering a > b in a lattice is called a singular cover if a is join irreducible and b is meet irreducible. A classification of the singular covers which occur in free lattices is given. AMS (MOS) subject classification (1980). 06B25.