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A subset of a model of PA is called neutral if it does not change the 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 PA. We show that cofinal extensions of prime models are neutrally expandable, and ω_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 lastarXiv:1712.06503v1 fatcat:vjlkes252bfnhdjj6t6itulrjy