A dependent theory with few indiscernibles

We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: For every θ there is a dependent theory T of size θ such that for all κ and δ, κ → (δ) _T,1 iff κ → (δ) _θ ^<ω . This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.