$\Pi _{1}^{0}$ Classes and Strong Degree Spectra of Relations

Journal of Symbolic Logic 72 (3):1003 - 1018 (2007)

Authors
Valentina Harizanov
George Washington University
Abstract
We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear ordering. Countable $\Pi _{1}^{0}$ subsets of 2ω and Kolmogorov complexity play a major role in the proof
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DOI 10.2178/jsl/1191333852
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References found in this work BETA

Intrinsically Gs;0alpha; Relations.E. Barker - 1988 - Annals of Pure and Applied Logic 39 (2):105-130.
Turing Degrees of Certain Isomorphic Images of Computable Relations.Valentina S. Harizanov - 1998 - Annals of Pure and Applied Logic 93 (1-3):103-113.
Uncountable Degree Spectra.Valentina S. Harizanov - 1991 - Annals of Pure and Applied Logic 54 (3):255-263.

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