Menachem Magidor - Taming the Monster of Independence

Mathematicians feel that every genuine mathematical problem has a solution. Gödel's incompleteness theorem is a major challenge to this feeling, because it claims that every rich enough mathematical theory contains a statement that can not be proved or disproved by this theory. Namely: the problem is independent of present theory. The result of the last half a century showed that many problems in many subfields of Mathematics are independent of the usual axiom system mostly used by mathematicians: ZFC. The most famous one is the Continuum Hypothesis, CH. Discovering that a problem you spent a lot of time and effort with, is independent, is very frustrating for the working mathematician. This is the source of the expression ” the monster of independence” . Can the ” ugly monster of independence” be tamed? Can we still find ways of settling problems that seem to be independent? In the talk we shall explore several approaches to this challenge.