Abstract
Abstract For the notion of degree of categoricity, we study an analogous notion for punctual structures. We show that such notions coincide for non- Δ 1 0 $\Delta _{1}^{0}$ normal upper Delta 1 Superscript 0 -categorical injection structures, and construct an example of a Δ 1 0 $\Delta _{1}^{0}$ normal upper Delta 1 Superscript 0 -categorical injection structure for which these notions differ. Additionally, we also show that in every non-zero c.e. Turing degree, there exists a PR-degree that is low for punctual isomorphism (to be defined), and also a PR-degree that is a degree of punctual categoricity.