This chapter presents the theorem of Kirby and Paris characterizing strong cuts in models of arithmetic. In the build up to the theorem, semiregular and regular cuts are also discussed. Other results in this chapter include a theorem on nonconservative minimal extensions and two important model theoretic characterizations of Peano Arithmetic, one due to Kaye and one to Wilkie.
Keywords: semiregular cuts, regular cuts, strong cuts, Kirby and Paris, nonconservative minimal extensions, Kaye, Wilkie