This project is only suitable for the fourth year 35 credit assignment, and in particular for students who have already taken the set theory course in their third year.
Moving on from what was covered in that course, the project may include an account of G\"odel's proof of the relative consistency of the generalized continuum hypothesis and the axiom of choice, Cohen's method of forcing, and an account of some of what is known about Suslin trees.
It would also be possible to give an account of the basics of large cardinals, for instance definition and basic properties of measurable cardinals.