Journal of Symbolic Logic

Π10 classes and strong degree spectra of relations

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