Abstract complexity theory and the Δ20 degrees Original Research Article

We show how Abstract Complexity Theory is related to the degrees of unsolvability and develop machinery by which computability theoretic hierarchies with a complexity theoretic flavor can be defined and investigated. This machinery is used to prove results both on hierarchies of View the MathML source sets and hierarchies of View the MathML source degrees. We prove a near-optimal lower bound on the effectivity of the Low Basis Theorem and a result showing that array computable c.e. degrees are, in some sense, the simplest possible View the MathML source degrees. We also examine the growth rates of iterates of View the MathML source. Finally, we indicate how complexity theory can be used to analyze notions of genericity intermediate between 1-genericity and 2-genericity, and produce a hierarchy of such notions.