  Such a sentence ϕ is called an Orey sentence with respect to T. We shall refer to this kind of independence as horizontal independence. Using metamathematical techniques one can construct such sentences. But again, as in the case of vertical independence, there are also natural non-metamathematical examples—for example, PU (the statement that the projective sets have the uniformization property, a property we shall discuss below) is a statement of (schematic) second-order arithmetic that is an Orey sentence with respect to ZFC, and CH is a statement of third-order arithmetic that is an Orey sentence with respect to ZFC. 