A generalization of Erd\H{o}s--Ko--Rado theorem to $t$-designs in   certain semilattices
  The Erd\H{o}s--Ko--Rado theorem is extended to designs in semilattices with certain conditions. As an application, we show the intersection theorems for the Hamming schemes, the Johnson schemes, bilinear forms schemes, Grassmann schemes, signed sets, partial permutations and restricted signed sets. 
Sho Suda
math.CO