Journal of Symbolic Logic

Π10 classes and strong degree spectra of relations

John Chisholm,Jennifer Chubb,Valentina S. Harizanov,Denis R. Hirschfeldt,Carl G., Jr. Jockusch,Timothy McNicholl, and Sarah Pingrey

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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 Π10 subsets of 2ω and Kolmogorov complexity play a major role in the proof.

Article information

Source
J. Symbolic Logic Volume 72, Issue 3 (2007), 1003-1018.

Dates
First available: 2 October 2007

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1191333852

Digital Object Identifier
doi:10.2178/jsl/1191333852

Mathematical Reviews number (MathSciNet)
MR2354911

Citation

Chisholm, John; Chubb, Jennifer; Harizanov, Valentina S.; Hirschfeldt, Denis R.; Jockusch, Carl G., Jr.; McNicholl, Timothy; Pingrey, Sarah. Π 1 0 classes and strong degree spectra of relations. Journal of Symbolic Logic 72 (2007), no. 3, 1003--1018. doi:10.2178/jsl/1191333852. http://projecteuclid.org/euclid.jsl/1191333852.


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