Forcing as a tool to prove theorems
Paul Cohen showed that the Continuum Hypothesis is independent of the usual axioms of set theory. His solution involved a new apparatus for constructing models of set theory - the method of *forcing*. As Cohen predicted, the method of forcing became very successful in establishing the independence of various statements from the usual axioms of set theory. What Cohen never imagined, is that forcing would be found useful in proving theorems.
In this talk, we shall present a few results in combinatorics whose proof uses the method of forcing, including our recent resolution of the infinite weak Hedetniemi conjecture.
The talk will be targeted to a general audience.