We show that for every computably enumerable (c.e.) degree a¿0 there is an intrinsically c.e. relation on the domain of a computable structure of computable dimension 2 whose degree spectrum is {0; a}, thus answering a question of Goncharov and Khoussainov (Dokl. Math. 55 (1997) 55-57). We also show
✦ LIBER ✦
Degree Spectra of Relations on Computable Structures in the Presence of Δ02Isomorphisms
✍ Scribed by Denis R. Hirschfeldt
- Book ID
- 124978615
- Publisher
- Association for Symbolic Logic
- Year
- 2002
- Tongue
- English
- Weight
- 505 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0022-4812
- DOI
- 10.2307/2694946
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## Abstract We investigate the computational complexity the class of Γ‐categorical computable structures. We show that hyperarithmetic categoricity is Π^1^~1~‐complete, while computable categoricity is Π^0^~4~‐hard. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)