Περίληψη:
In this paper, we prove results concerning the existence of proper end extensions of arbitrary models of fragments of Peano arithmetic (PA). In particular, we give alternative proofs that concern (a) a result of Clote (Fundam Math 127(2):163–170, 1986); (Fundam Math 158(3):301–302, 1998), on the end extendability of arbitrary models of Σ n-induction, for n≥ 2 , and (b) the fact that every model of Σ 1-induction has a proper end extension satisfying Δ -induction; although this fact was not explicitly stated before, it follows by earlier results of Enayat and Wong (Ann Pure Appl Log 168:1247–1252, 2017) and Wong (Proc Am Math Soc 144:4021–4024, 2016). © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
