A cartesian presentation of weak n-categories

We propose a notion of weak (n + k, n)-category, which we call (n + k, n)-Theta-spaces. The (n + k, n)-Theta-spaces are precisely the fibrant objects of a certain model category structure on the category of presheaves of simplicial sets on Joyal's category Theta(n). This notion is a generalization of that of complete Segal spaces (which are precisely the (infinity, 1)-Theta-spaces). Our main result is that the above model category is cartesian.