Abstract
This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class of structures of Scott rank , the class of structures of Scott rank , and the class of all structures of non-computable Scott rank. We show that is -complete , is -complete relative to Kleene’s , and is -complete \mathcal{O}$.
Citation
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
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