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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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.

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

First available in Project Euclid: 2 October 2007

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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. J. Symbolic Logic 72 (2007), no. 3, 1003--1018. doi:10.2178/jsl/1191333852.

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