On large systems of sets with no large weak delta-subsystems

A family of sets is called a weak Delta-system if the cardinality of the in tersection of any two sets is the same. We elaborate a construction by Rodl and Thoma [9] and show that for large n, there exists a family F of subset s of {1,..., n} without weak Delta-systems of siae 3 with \F\greater than o r equal to 2(c(n log n)1/3).