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.
From: Dino Rossegger [view email]
[v1]
Sat, 13 Jun 2026 08:46:08 UTC (26 KB)
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