I'm a beginner in descriptive set theory.

There is a series of connected exercises (1C.6, 1C.7, 1C.8) in Moschovakis' classic text (new edition) on uniformization. They are simple case uniformization, reduction (by uniformization), and separation of sets (via reduction).

It seems like with such layout, the point of uniformization is to give us a way to separate sets.

My question is, why are we interested in uniformization and reduction? What I can see is that uniformization can always be carried out with AC, pretty obvious. So, has it anything to do with Choice?

What about reduction?