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Relative to any non-hyperarithmetic set
Journal of Mathematical Logic 13 (1):1250007 (2013)
Abstract
We prove that there is a structure, indeed a linear ordering, whose degree spectrum is the set of all non-hyperarithmetic degrees. We also show that degree spectra can distinguish measure from category.Links
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2012-11-26
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2012-11-26
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Citations of this work
Continuous higher randomness.Laurent Bienvenu, Noam Greenberg & Benoit Monin - 2017 - Journal of Mathematical Logic 17 (1):1750004.
An Effective Analysis of the Denjoy Rank.Linda Westrick - 2020 - Notre Dame Journal of Formal Logic 61 (2):245-263.
A Local Version of the Slaman–Wehner Theorem and Families Closed Under Finite Differences.Marat Faizrahmanov - 2023 - Notre Dame Journal of Formal Logic 64 (2):197-203.
References found in this work
Pairs of recursive structures.C. J. Ash & J. F. Knight - 1990 - Annals of Pure and Applied Logic 46 (3):211-234.
Enumerations in computable structure theory.Sergey Goncharov, Valentina Harizanov, Julia Knight, Charles McCoy, Russell Miller & Reed Solomon - 2005 - Annals of Pure and Applied Logic 136 (3):219-246.
Recursively presentable prime models.Leo Harrington - 1974 - Journal of Symbolic Logic 39 (2):305-309.
Realizing Levels of the Hyperarithmetic Hierarchy as Degree Spectra of Relations on Computable Structures.Walker M. White & Denis R. Hirschfeldt - 2002 - Notre Dame Journal of Formal Logic 43 (1):51-64.
Degree spectra and immunity properties.Barbara F. Csima & Iskander S. Kalimullin - 2010 - Mathematical Logic Quarterly 56 (1):67-77.
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