turkmath.org

An effectively closed set, i.e. Pi^0_1 class, may be viewed as the set of infinite paths through a computable tree. Complexity of members of effectively closed sets has resulted in rich and well developed theory. We give recent results on Turing degrees of members of such classes. Although some familiarity with the notion of Turing computability would help, we shall first review basic recursion theoretic notions and then introduce effectively closed sets with its applications in mathematics.