Search Results for ""

In nonstandard analysis, the limitation to first-order analysis can be avoided by using a construction known as a superstructure. Superstructures are constructed in the ...

This problem is NP-complete (Garey and Johnson 1983).

Suppose <= is a partial ordering on a nonempty set A. Then the elements a,b in A are said to be comparable provided a<=b or b<=a. Because two elements in a partially ordered ...

Let X be a set of urelements that contains the set N of natural numbers, and let V(X) be a superstructure whose individuals are in X. Let V(^*X) be an enlargement of V(X), ...

A set R of linear extensions of a partially ordered set P=(X,<=) is a realizer of P (and is said to realize P) provided that for all x,y in X, x<=y iff x is below y in every ...

Two totally ordered sets (A,<=) and (B,<=) are order isomorphic iff there is a bijection f from A to B such that for all a_1,a_2 in A, a_1<=a_2 iff f(a_1)<=f(a_2) (Ciesielski ...

The largest value of a set, function, etc. The maximum value of a set of elements A={a_i}_(i=1)^N is denoted maxA or max_(i)a_i, and is equal to the last element of a sorted ...

The smallest value of a set, function, etc. The minimum value of a set of elements A={a_i}_(i=1)^N is denoted minA or min_(i)a_i, and is equal to the first element of a ...

Consider a Boolean algebra of subsets b(A) generated by a set A, which is the set of subsets of A that can be obtained by means of a finite number of the set operations ...

The comparability graph of a partially ordered set P=(X,<=) is the graph with vertex set X for which vertices x and y are adjacent iff either x<=y or y<=x in P.