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arXiv · 2606.15196

Structural vs. computational complexity

Johanna N. Y. Franklin·Dino Rossegger·Dan Turetsky
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Abstract

We consider highness in the context of computable structure theory and, particularly, the Scott rank of a structure. We define highness for Scott rank and highness for computably defined Scott rank $\alpha$ and characterize them in terms of the ability to compute $\Delta^0_\beta$ sets for appropriate $\beta$. We close with a discussion of the index sets of structures with a given Scott rank or computably defined Scott rank and a few words about highness for noncomputable Scott ranks.

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BibTeXRIS

Johanna N. Y. Franklin, Dino Rossegger, Dan Turetsky. 2026-06-13. Structural vs. computational complexity. https://arxiv.org/abs/2606.15196

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