r-Maximal Sets

Eberhard Herrmann

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 60

MSC 2000

03D25 Recursively (computably) enumerable sets and degrees

The r-maximal sets and their properties were investigated in several papers. Here it will be given a systematical presentation of all these results including also few which are still not published. In the centre of interest are the atomless, r-maximal sets and the different methods of constructing them. In particular in the paper are treated the already known lattice properties of the r-maximal sets. But also degree properties of them and more general of the r-cohesive sets are given. Further the paper includes also index set estimations of special classes of r-maximal sets and considers the relationship between classes of r-maximal sets and other classes of c.e. sets.

Keywords: computable enumerable set, lattice of c.e. sets, r-maximal sets, r-cohesive set, c.e. superset structure, indexsets, monotone set, r-maximal major subset