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 order. Countable Π01 subsets of 2w and Kolmogorov complexity play a major role in the proof.
Chisholm, John; Chubb, Jennifer; Harizanov, Valentina S.; Hirschfeldt, Denise R.; Jockusch, Carl G.; McNicholl, Timothy H.; and Pingrey, Sarah, "Π01 Classes and Strong Degree Spectra of Relations" (2007). Mathematics. 2.