Maxwell Levine : The Essentials of Forcing

Posted by Maxwell Levine , part of the Graduate Student Colloquium.

At

Nov. 9, 2015, 4 p.m.

In

BH 209

Abstract

Georg Cantor lost his mind trying to prove his continuum hypothesis: that there is no set with a cardinality strictly between that of the natural numbers and the real numbers. But nearly a century later Paul Cohen demonstrated that the continuum hypothesis could neither be proved nor refuted by the standard Zermelo-Fraenkel axioms of set theory. The technique he invented, called forcing, is a way of constructing new models of set theory by adjoining transcendental elements to the old models. In this talk I will outline the general methodology of forcing and give a sense of the technical obstacles it must overcome.