Metamathematical Methods in Descriptive Set Theory

(Under construction)

In this project, I survey a number of proofs in descriptive set theory that make use of metamathematical methods. On the I hand, I aim to give a classification as to what methods are used and how they are used, and how seriously they are involved in the proofs. On the other hand, I attempt to draw more general conclusions about the practice of differentiating proofs by their methods: e.g., what criteria do we ascribe to a collection of tools and techniques, such that it can be deemed a sui generis method? Under what circumstances may we say two proofs use the same method? The hope is to use this case study to clarify some of the practices in mathematics where one desires a proof by a certain method or where one dismisses a proof as new because it is just a rehash of an old proof by a different method.