DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE ODENSE UNIVERSITY Set-Pair Method in Extremal Set Theory Benjamin Sudakov School of Mathematical Sciences Tel Aviv University Tuesday, February 13, 1996, at 2:15 PM The Seminar Room Let S = { (A_i,B_i) | 1 <= i <= m } be a set system such that |A_i|=a, |B_i|=b and, for all i,j, A_i and B_j are disjoint if and only if i=j. B. Bolobas proved that the size of S is at most (a+b) choose b. We will discuss applications of this result and its generalizations to extremal set theory. Gregory Gutin