Neutrally Expandable Models of Arithmetic

Abstract

A subset of a model of $\mathsf{PA}$ is called neutral if it does not change the $\mathrm{dcl}$ relation. A model with undefinable neutral classes is called neutrally expandable. We study the existence and non-existence of neutral sets in various models of $\mathsf{PA}$. We show that cofinal extensions of prime models are neutrally expandable, and ${\omega }_1$-like neutrally expandable models exist, while no recursively saturated model is neutrally expandable. We also show that neutrality is not a first-order property. In the last section, we study a local version of neutral expandability.

References in corpus (1)

• Enayat Models of Peano Arithmetic