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December 2007 Index sets for classes of high rank structures
W. Calvert, E. Fokina, S. S. Goncharov, J. F. Knight, O. Kudinov, A. S. Morozov, V. Puzarenko
J. Symbolic Logic 72(4): 1418-1432 (December 2007). DOI: 10.2178/jsl/1203350796

Abstract

This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class $K_{\omega^{CK}_1}$ of structures of Scott rank $\omega^{CK}_1$, the class $K_{\omega^{CK}_1+1}$ of structures of Scott rank $\omega^{CK}_1+1}$, and the class $K$ of all structures of non-computable Scott rank. We show that $I(K)$ is $m$-complete $\Sigma^1_1$, $I(K_{\omega^{CK}_1})$ is $m$-complete $\Pi^0_2$ relative to Kleene’s $\mathcal{O}$, and $I(K_{\omega^{CK}_1+1})$ is $m$-complete $\Sigma^0_2 relative to $\mathcal{O}$.

Citation

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W. Calvert. E. Fokina. S. S. Goncharov. J. F. Knight. O. Kudinov. A. S. Morozov. V. Puzarenko. "Index sets for classes of high rank structures." J. Symbolic Logic 72 (4) 1418 - 1432, December 2007. https://doi.org/10.2178/jsl/1203350796

Information

Published: December 2007
First available in Project Euclid: 18 February 2008

zbMATH: 1145.03021
MathSciNet: MR2371215
Digital Object Identifier: 10.2178/jsl/1203350796

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 4 • December 2007
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