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arXiv · 2603.08010

Primitive recursive categoricity spectra of functional structures

Nikolay Bazhenov·Heer Tern Koh·Keng Meng Ng
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Abstract

For the notion of degree of categoricity, we study an analogous notion for punctual structures. We show that such notions coincide for non-$\Delta_{1}^{0}$-categorical injection structures, and construct an example of a $\Delta_{1}^{0}$-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.

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Nikolay Bazhenov, Heer Tern Koh, Keng Meng Ng. 2026-03-09. Primitive recursive categoricity spectra of functional structures. https://arxiv.org/abs/2603.08010

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