Noah Schoem : On Hilbert's First Problem, or Why the Continuum Hypothesis Isn't Obviously False

Posted by Noah Schoem , part of the Graduate Student Colloquium.

At

April 12, 2018, 5 p.m.

In

SEO 636

Abstract

In 1878, Georg Cantor proved that there are more real numbers than natural numbers, and asked whether there is a size strictly in between. Cantor conjectured that there isn't, and called this conjecture the Continuum Hypothesis. Nearly a century later, the combined works of Gödel and Cohen proved this question mathematically impossible to resolve; the methods they used shaped the foundations of modern set theory into what it is today. After a brief background on what we mean by mathematically impossible to resolve, we will explore Gödel's contribution, The Constructible Universe (and the foundations of Inner Model Theory), in which the Continuum Hypothesis is true.

There will be pizza.