Intersection Theorems for Systems of Finite Sets

Notation The letters a, b, c, d, x, y, z denote finite sets of non-negative integers, all other lower-case letters denote non-negative integers. If fc I, then [k, I) denotes the set k, k+l, k+2,. . . , l-l = {*: fc < « < Q. The obliteration operator serves to remove from any system of elements the element above which it is placed. Thus [k, I) = {k, k-{-l,. . . , fy. The cardinal of o is inclusion (in the wide sense), union, difference, and intersection of sets are denoted by o c b, a-\-b, a—b, ab respectively, and a—b = a—ab for all a, b. By 8 (k, l, m) we denote the set of all systems (ao, av. . . , dn) such that avc[0, m) ; 1 (v < »),