 The concept of a “world” in the MWI belongs to part (ii) of the theory, i.e., it is not a rigorously defined mathematical entity, but a term defined by us (sentient beings) to describe our experience. When we refer to the “definite classically described state” of, say, a cat, it means that the position and the state (alive, dead, smiling, etc.) of the cat is specified according to our ability to distinguish between the alternatives, and that this specification corresponds to a classical picture, e.g., no superpositions of dead and alive cats are allowed in a single world.