I gave a colloquium talk at Bar-Ilan University on November 10, 2013.
Paul Cohen celebrated solution to Hilbert’s first problem 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 (that is, implications).
In this talk, we shall motivate the forcing machinery, and then present a collection of results that were proved using the method of forcing.
The talk was intended for a general audience, and comments are very welcome.