On Models Constructed by Means of the Arithmetized Completeness Theorem
Richard W. Kaye, Henryk Kotlarski · Mathematical logic quarterly · 2000
In this paper we study the model theory of extensions of models of first-order Peano Arithmetic (PA) by means of the arithmetized completeness theorem (ACT) applied to a definable complete extension of PA in the original model. This leads us to many interesting model theoretic properties equivalent to reflection principles and ω-consistency, and these properties together with the associated first-order schemes extending PA are studied.