INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS

2. 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 \a\\ 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); \av\ 1 (v < »),