An American in Oxford taking a Set Theory course

Thread 1/

When writing my dissertation in philosophy, I spent time in Oxford working with my supervisor Joseph Raz. For the fun of it, I decided to take an advanced course on set theory. It on the independence of the Continuum Hypothesis. 2/

The Continuum Hypothesis (CH) states that there are no sets of infinite cardinality that are larger than the rationals but smaller than the reals. In short, there are the rational numbers and the real numbers and nothing in between. The course I wanted to take was on the CH. 3/

I've forgotten the teacher's name, but he was well-known. I think he won the Fields Medal early in his career. He was a typical Oxford don--terrible lecturer, covered head-to-toe in chalk and very pasty. But he was super smart and nice 4/

The material was hard. We spent the semester going through Cohen's proof of the independence of the CH using the technique of forcing. Essentially, what Cohen proved is that standard set theory does not settle the question of the CH. In some models, there are intermediate 5/

size sets between the rationals and reals, others not. The CH is independent of the ZFC axioms much like the parallel hypothesis is independent of Euclidean Geometry. The difficulty of the material was compounded by the professor's old-fashioned notation. 6/

Instead of using the standard upside down A for universal quantification, he used the large caret ^. For existential quantification, he used the large V instead of backwards E. So in addition to trying to follow the proofs, I had to translate notation on the fly. 7/

The professor also spoke quickly and at the blackboard. So I would routinely interrupt him by asking him to clarify his steps. I asked so many questions, and no one else did, that he started lecturing just to me. 8/

At the end of the semester, a British student came up to me and asked for help with the material. He said that his study group picked me as the person to approach. I was flabbergasted. I barely could follow the lectures. 9/

"Haven't you seen me ask tons of questions the whole semester?" "Yes," he replied. "That's why we picked you. Only the smartest kid in the class is allowed to ask questions. And he lectures only to you." America and Britain--two people separated by a common formalism. /fin