This will be a reading seminar on the method of forcing.

In the first part of the course will develop the method of forcing and prove the independence of the Continuum Hypothesis from ZFC, and the independence of the Axiom of Choice from ZF. We will cover several technical notions which are crucial for modern day set theory, including: chain conditions; closure and distributivity conditions; product forcing and mutual genericity; collapse forcing; projections and isomorphism of forcing notions.

Given time, we will continue to more advanced applications of forcing, in particular to descriptive set theory. We will start with proving the consistency of ZF + DC + 'all sets of reals are Lebesgue measurable', assuming the existence of an inaccessible cardinal (the Solovay Model).

The evaluation will be based on seminar presentations and one written assignment. The precise number of presentations will depend on the number of participants.