 Cross-world Duplication  \(x\) as it is at \(w\) is a duplicate of \(y\) as it is at \(w'\) if and only if there is a one-to-one function \(f\) whose domain includes everything that is part of \(x\) at \(w\), and whose range includes everything that is part of \(y\) at \(w'\), such that for any sequence \(x_1,\ldots,x_n\) of objects that are parts of \(x\) at \(w'\) and perfectly natural \(n\)-ary relation \(R\), \(x_1,\ldots,x_n\) instantiate \(R\) at \(w\) if and only if \(f(x_1),\ldots,f(x_n)\) instantiate \(R\) at  \(w'\).[20] 