 Kripke shows how to build up \(\mathcal{E}\) and \(\mathcal{A}\) by an inductive process. One starts with an ‘approximation’ of the extension and anti-extension of \(\Tr\), and successively improves it until the improvement process ceases to be productive (it reaches a ‘fixed point’). In fact, for the \(K_3\)-based solution, the natural thing to do is start with an empty extension and anti-extension, and throw in sentences that are true at successive stages of the process.