Π10 classes and strong degree spectra of relations
John Chisholm, Jennifer Chubb, Valentina Harizanov, Denis R. Hirschfeldt, Carl G. Jockusch, Timothy H. McNicholl, Sarah Pingrey · Journal of Symbolic Logic · 2007
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 subsets of 2ω and Kolmogorov complexity play a major role in the proof.