Intersection theorems for systems of finite vector spaces

A theorem of Erdos, Ko and Rado states that if S is an n-element set and F is a family of k-element subsets of S, k= = 2k, ...F... = = 2k + 1, ...F... = = 2k + 2 and n >= 2k + 1, q >= 3. Application of these methods to the analogous subset problem leads to improvement on the Erdos-Ko-Rado bounds.