Abstract

In this paper, we prove results concerning the existence of proper end extensions of arbitrary models of fragments of Peano arithmetic. In particular, we give alternative proofs that concern a result of Clote :163–170, 1986); :301–302, 1998), on the end extendability of arbitrary models of \-induction, for \, and the fact that every model of \-induction has a proper end extension satisfying \-induction; although this fact was not explicitly stated before, it follows by earlier results of Enayat and Wong and Wong.