Two Embedding Theorems for Finite Lattices

Convergence Theorems For Two Finite Families of Uniformly L-Lipschitzian Mappings

FUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY DISTRIBUTIVE LATTICES

The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...

Embedding Finite Lattices into the Computably Enumerable Degrees — a Status Survey

We survey the current status of an old open question in classical computability theory: Which finite lattices can be embedded into the degree structure of the computably enumerable degrees? Does the collection of embeddable finite lattices even form a computable set? Two recent papers by the second author show that for a large subclass of the finite lattices, the so-called join-semidistributive...

A Survey of Tensor Products and Related Constructions in Two Lectures

We survey tensor products of lattices with zero and related constructions focused on two topics: amenable lattices and box products. PART I. FIRST LECTURE: AMENABLE LATTICES Abstract. Let A be a finite lattice. Then A is amenable (A⊗B is a lattice, for every lattice B with zero) iff A (as a join-semilattice) is sharply transferable (whenever A has an embedding φ into IdL, the ideal lattice of a...

2 2 Ja n 20 05 EMBEDDING FINITE LATTICES INTO FINITE BIATOMIC LATTICES

For a class C of finite lattices, the question arises whether any lattice in C can be embedded into some atomistic, biatomic lattice in C. We provide answers to the question above for C being, respectively, — The class of all finite lattices; — The class of all finite lower bounded lattices (solved by the first author's earlier work). — The class of all finite join-semidistributive lattices (th...