The generic degrees of density-1 sets, and a characterization of the hyperarithmetic reals (Q2795919)

The paper is devoted to the study of generic computations -- the motivation for the latter is derived from complexity theory. It is shown that generic reduction is \(\Pi_{1}^{1}\)-complete. Therefore the author works with the generic degrees of density-1 reals. It is demonstrated how an understanding of these degrees leads to a greater understanding of the overall structure of the generic degrees. The density-1 sets are used to provide a new characterization of the hyperarithmetical Turing degrees.