Η-representation of sets and degrees
Journal of Symbolic Logic 73 (4):1097-1121 (2008)
Abstract
We show that a set has an η-representation in a linear order if and only if it is the range of a 0'-computable limitwise monotonic function. We also construct a Δ₃ Turing degree for which no set in that degree has a strong η-representation, answering a question posed by DowneyDOI
10.2178/jsl/1230396908
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Citations of this work
A Friedberg enumeration of equivalence structures.Rodney G. Downey, Alexander G. Melnikov & Keng Meng Ng - 2017 - Journal of Mathematical Logic 17 (2):1750008.
Computable Abelian groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.
Increasing η ‐representable degrees.Andrey N. Frolov & Maxim V. Zubkov - 2009 - Mathematical Logic Quarterly 55 (6):633-636.
Limitwise monotonic functions, sets, and degrees on computable domains.Asher M. Kach & Daniel Turetsky - 2010 - Journal of Symbolic Logic 75 (1):131-154.
Automorphisms of η -like computable linear orderings and Kierstead's conjecture.Charles M. Harris, Kyung Il Lee & S. Barry Cooper - 2016 - Mathematical Logic Quarterly 62 (6):481-506.
References found in this work
Computable Models of Theories with Few Models.Bakhadyr Khoussainov, Andre Nies & Richard A. Shore - 1997 - Notre Dame Journal of Formal Logic 38 (2):165-178.
Bounding Prime Models.Barbara F. Csima, Denis R. Hirschfeldt, Julia F. Knight & Robert I. Soare - 2004 - Journal of Symbolic Logic 69 (4):1117 - 1142.
Order-Computable Sets.Denis Hirschfeldt, Russell Miller & Sergei Podzorov - 2007 - Notre Dame Journal of Formal Logic 48 (3):317-347.
