Title: "On set systems with a threshold property".

K. Takata (University of Illinois at Chicago)

For n, k and t such that 1 < t < k < n, a set F of subsets of [n]  has the
(k,t)-{threshold property} if every k-subset of [n] contains at least t sets
from the set system F and every (k-1)-subset of [n] contains less than t sets
from F.  The minimal number of sets in a set system with this property is
denoted  by m(n, k, t).  In this paper we determine m(n, 4, 3) exactly for n
sufficiently large, and we show that m(n, k, 2) is asymptotically  equal to the
generalized Turan number T_{k-1}(n, k, 2).

Joint work with Z. F"uredi, R. H. Sloan, and Gy. Tur'an