Chennai Mathematical Institute


Research seminar by MSc students
11:50 - 1:05, Seminar Hall
Forcing and continuum hypothesis (CH)

Raiean Banerjee
Chennai Mathematical Institute.


In this talk my main focus is to explain Forcing and it’s arguably most famous application for which Paul Cohen received his Fields Medal. At first I will state CH and the long term beliefs which people like Cantor held about it before Cohen’s work. Then I will explain what is meant by “Independence” and will give some very simple examples of “Independent Statements”. Then, I will explain the concept of “Consistency” and “Relative Consistency” and the relation between these two concepts and “Independence”. Then, I will explain the intuition (as per my observations) behind the concept of “Forcing”. This will be followed by the explanation of “forcing” itself and its application in Cohen’s proof of the fact that negation of CH is consistent with ZFC. This will be the main aim of this talk. In this talk I will assume the consistency of CH with ZFC, which was proved by Kurt Godel with the help of his “Constructible Universe” (Infact, Godel proved a stronger statement than this, but for this talk we don’t need the general statement). But, if time permits then, I can also throw some light in a heuristic manner on Godel’s proof which I have already mentioned above.