Recursion theory : computational aspects of definability
Recursion theory e-böcker
Walter de Gruyter GmbH & Co., KG
2015
EISBN 9783110275643
Part I: Fundamental theory.
Part II: The story of turing degrees.
Part III: Hyperarithmetic degrees and perfect set properly.
Part IV: Higher randomness theory.
This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion theory. These include structure theory, hyperarithmetic determinacy and rigidity, basis theorems, independence results on Turing degrees, as well as applications to higher randomness.
Part II: The story of turing degrees.
Part III: Hyperarithmetic degrees and perfect set properly.
Part IV: Higher randomness theory.
This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion theory. These include structure theory, hyperarithmetic determinacy and rigidity, basis theorems, independence results on Turing degrees, as well as applications to higher randomness.
