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.
"Π10 classes and strong degree spectra of relations." J. Symbolic Logic 72 (3) 1003 - 1018, September 2007. https://doi.org/10.2178/jsl/1191333852