Realizing Levels of the Hyperarithmetic Hierarchy as Degree Spectra of Relations on Computable Structures

We construct a class of relations on computable structures whose degree spectra form natural classes of degrees. Given any computable ordinal and reducibility r stronger than or equal to m-reducibility, we show how to construct a structure with an intrinsically invariant relation whose degree spectrum consists of all nontrivial r-degrees. We extend this construction to show that can be replaced by either or
Keywords degree spectra of relations   computable structures   computable model theory   hyperarithmetic hierarchy
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DOI 10.1305/ndjfl/1071505769
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Relative to Any Non-Hyperarithmetic Set.Noam Greenberg, Antonio Montalbán & Theodore A. Slaman - 2013 - Journal of Mathematical Logic 13 (1):1250007.

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