Pairs of partially ordered sets of tame representation type

Tripled partially ordered sets

In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

Some Representation Theorems for Partially Ordered Sets

Ordering Subsets of (partially) Ordered Sets: Representation Theorems

In many practical situations, we have a (partially) ordered set V of different values. For example, we may have the set of all possible values of temperature, or the set of all possible degrees of confidence in a statement. In practice, we are often uncertain about the exact value of the quantity. Due to this uncertainty, at best, we know a set S ⊆ V of possible values of the quantity: e.g., an...

Completion of Partially Ordered Sets

The paper considers a generalization of the standard completion of a partially ordered set through the collection of all its lower sets.

Endomorphisms of Partially Ordered Sets

Let P be a partially ordered set. A function φ : P → P is an endomorphism of P if for every two elements x, y of P , the inequality φ(x) 6 φ(y) holds whenever x 6 y. Obviously, the identity mapping is a (trivial ) endomorphism. Here, however, we will be interested in endomorphisms with an image of size less than |P |, i.e. endomorphisms which are not automorphisms of P . We will refer to them a...