 The resulting partially ordered sets should also have the property that sequences of approximations, in particular infinite chains \(x_0 \sqsubseteq x_1 \sqsubseteq \ldots\) should converge to a limit containing the information cumulatively provided by the \(x_i\). The same structure is also exploited in Kleene’s proof of the First Recursion Theorem in Kleene 1952 (secs. 66, 348–50), and will allow to define a notion of continuous function in terms of preservation of limits.