Athar Abdul-Quader, Roman Kossak
Published 2017-12-18Version 1
A subset of a model of ${\sf PA}$ 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 ${\sf PA}$. 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.
On Non-standard Models of Arithmetic with Uncountable Standard Systems
The complexity of classification problems for models of arithmetic
The Kaufmann--Clote question on end extensions of models of arithmetic and the weak regularity principle
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