Abstract: A set S is said to be 3-term A.P free if there are no elements in S which form a 3-term A.P.In first part of talk, we will see a greedy way of constructing a 3-term A.P free set S.In the later part, we state and prove Behrend's theorem which shows that there exists set A(subset of [N]) which is 3-term free s.t |A|>>N.exp(-csqrt(logN)) for some c>0.
