Primitive recursive categoricity spectra of functional structures

Abstract

For the notion of degree of categoricity, we study an analogous notion for punctual structures. We show that such notions coincide for non-$\hat{I}{”}_1^0$-categorical injection structures, and construct an example of a $\hat{I}{”}_1^0$-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.