Turing Degrees: The Structure of Relative Computability

In this video, I introduce the Turing Degrees. Recursion theorists are interested in studying relative computability: if a computer had magical access to one noncomputable function, what other functions would it be able to compute? This gives us an "is more powerful than" ordering on functions, and the question is, what structural properties does this ordering have?

00:00 Introduction to Computability
07:03 Constructing a Noncomputable Function
10:10 Oracles
12:23 Relative Computability
16:33 Turing Jump
18:09 Constructing Incomparable Degrees
25:14 Conclusion

I referenced the proof of the existence of incomparable Turing degrees from S. Barry Cooper's "Computability Theory". This is from a list of references I got asking about the proof on math.stackexchange: https://math.stackexchange.com/questions/4940857/reading-on-incomparable-turing-degrees

I mention some properties of Turing Degrees that I found on Wikipedia. You can find other properties there as well: https://en.wikipedia.org/wiki/Turing_degree

You can also find a list of properties of Turing degrees here: https://math.stackexchange.com/a/1327620/908546