Index Sets for Classes of High Rank Structures

Journal of Symbolic Logic 72 (4):1418 - 1432 (2007)

Authors
Artem Morozov
Moscow State University
Abstract
This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class $K_{\omega _{1}^{\mathit{CK}}}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}$ , the class $K_{\omega _{1}^{\mathit{CK}}+1}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}+1$ , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete $\Sigma _{1}^{1},\,I(K_{\omega _{1}^{\mathit{CK}}})$ is m-complete $\Pi _{2}^{0}$ relative to Kleen's O, and $I(K_{\omega _{1}^{\mathit{CK}}+1})$ is m-complete $\Sigma _{2}^{0}$ relative to O
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DOI 10.2178/jsl/1203350796
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References found in this work BETA

Pairs of Recursive Structures.C. J. Ash & J. F. Knight - 1990 - Annals of Pure and Applied Logic 46 (3):211-234.
Scott Sentences and Admissible Sets.Mark Nadel - 1974 - Annals of Pure and Applied Logic 7 (2):267.
On the Complexity of Categoricity in Computable Structures.Walker M. White - 2003 - Mathematical Logic Quarterly 49 (6):603.

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