Consistent amalgamation for þ-forking

In this paper, we prove the following:TheoremLet M be a rosy dependent theory and let p(x,a0), p(x,a1)be non-þ-forking extensions of p(x)∈S(A)with a0a1; assume that p(x,a0)∪p(x,a1)is consistent and that a0, a1start a þ-independent indiscernible sequence. Then p(x,a0)∪p(x,a1)is a non-þ-forking extension of p(x).We also provide an example to show that the result is not true without assuming NIP.