Results from the rich and well-developed theory of well-quasi-ordering have often been rediscovered and republished. The purpose of this paper is to describe this intriguing subject. To illustrate the theory, here are two definitions and an elementary result. A partially ordered set is called well-partially-ordered if every subset has at least one, but only a finite number, of minimal elements....

Lattice games are real-valued functions de...ned on a ...nite lattice L. The basic players are the nonzero join-irreducible elements of the lattice and the coalitions are its elements. If L is the Boolean algebra 2 then we obtain a n-person game. Gilboa and Lehrer introduced the global games, which are lattice games where L = ¦n, the lattice of all partitions of N ordered by re...nement. Faigle...

Given a finite partially ordered set B, it is often of interest to describe the largest possible subsets SC B which consist of mutually incomparable elements of B. Such subsets are usually called maximum antichains or maximum Sperner families of .P after Sperner [I 51, who first characterized these maximum antichains in the case that 9 is a finite Boolean lattice, i.e., the set of all subsets o...

To take into account that expert’s degrees of certainty are not always comparable, researchers have used partially ordered set of degrees instead of the more traditional linearly (totally) ordered interval [0, 1]. In most cases, it is assumed that this partially ordered set is a lattice, i.e., every two elements have the greatest lower bound and the least upper bound. In this paper, we prove a ...

First, we establish a useful characterization of effective sets in conditionally complete partially ordered sets. Then, we prove that each maximal nonexpansive partial multiplier on a conditionally complete and infinitely distributive partially ordered set with upper bounded centre is inner. Finally, we show that some analogous results hold for T1-families of sets partially ordered by inclusion.

Dict ionary definitions are logical combina t ions of basic markers. Defini t ions can be reduced to dis junct ions of meanings, which are conjunct ions of markers . T h e set of words which can take on a m e a n i n g is its lexical representation set, and u n d e r natura l condi t ions such sets are partially ordered by inc lus ion in the same way as the mean i ngs are ordered by implicat io...

The results' in this paper were motivated by a search for the answers to the following questions : When can a given partially ordered algebra be embedded in a complete partially ordered algebra in such a fashion that the original algebra is dense and that the operations acquire or maintain continuity properties? What type of identities are preserved under such embeddings? Properties of extensio...

A Jbre F of a partially ordered set P is a subset which intersects each nontrivial maximal antichain of P. Let I be the smallest constant such that each finite partially ordered set P contains a fibre of size at most I ‘1 PI. We show that 1, < 3 by finding a good 3-coloring of the nontrivial antichains of P. Some decision problems involving iibres are also considered. For instance, it is shown ...