Primitive recursive categoricity spectra of functional structures
Logic
2026-03-10 v1
Abstract
For the notion of degree of categoricity, we study an analogous notion for punctual structures. We show that such notions coincide for non--categorical injection structures, and construct an example of a -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.
Keywords
Cite
@article{arxiv.2603.08010,
title = {Primitive recursive categoricity spectra of functional structures},
author = {Nikolay Bazhenov and Heer Tern Koh and Keng Meng Ng},
journal= {arXiv preprint arXiv:2603.08010},
year = {2026}
}