Difference Splittings of Recursively Enumerable Sets

Asat Arslanov (Computer Science Department, The University of Auckland, New Zealand)

Abstract: We study here the degree-theoretic structure of set-theoretical splittings of recursively enumerable (r.e.) sets into differences of r.e. sets. As a corollary we deduce that the odering of wtt-degrees of unsolvability of differences of r.e. sets is not a distributive semilattice and is not elementarily equivalent to the ordering of r.e. wtt-degrees of unsolvability.