Pi(0)(1) choice classes

摘要

We study the degree spectrum properties of so called Pi(0)(1) choice classes. A Pi(0)(1) choice class is a Pi(0)(1)class in which no two members have the same Turing degree. This definition leads us to some interesting cardinality properties, basis results and technically innovative constructions which might give us an insight to construct new Pi(0)(1) classes. The presented work can be considered as Pi(0)(1) choice class analogue of the work by Kent and Lewis [15]. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim