AN INTERSECTION THEOREM FOR SYSTEMS OF SETS

Erdos and Rado defined a Delta-system, as a family in which every two members have the same intersection. Here we obtain a new upper bound o n the maximum cardinality phi(n, q) of an n-uniform family not contain ing any Delta-system of cardinality q. Namely, we prove that, for any alpha > 1 and q, there exists C = C(alpha, q) such that, for any n, ph i(n,q) less than or equal to Cn !((log log log n)(2)/alpha log log n)( n). (C) 1996 John Wiley & Sons, Inc.