Noah Schoem : Class forcing and Easton's Theorem

Posted by Noah Schoem , part of the Louise Hay Logic Seminar.

At

Nov. 17, 2016, 4 p.m.

In

SEO 427

Abstract

Cohen (1963) proved $Con(ZFC)\implies Con\left(ZFC+2^{\aleph_0}=\aleph_2\right)$ using the method of forcing. Further work showed that $Con(ZFC)\implies Con\left(ZFC+2^{\aleph_0}=\kappa\right)$ for any $\kappa$ of uncountable cofinality. This raises the question of how the continuum function $\kappa\mapsto 2^\kappa$ can behave, which has been answered for regular cardinals (Easton 1970). We will cover Easton's Theorem and the techniques required to prove it, namely class-sized forcing and product forcing with Easton support.