Turing degrees

Turing degrees are a way to classify problems based on how computationally difficult they are, specifically in terms of their solvability by algorithms. Two problems share the same Turing degree if an algorithm exists that can solve one when given the solution to the other, meaning they are computationally equivalent in difficulty. If no such algorithm exists, they are in different degrees. This concept helps mathematicians understand the relative complexity of problems and how they’re interconnected within computability theory. Essentially, Turing degrees organize problems into levels of difficulty based on their algorithmic solvability.