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Demonstrating Independence: Forcing for Beginners

After Georg Cantor proved that the cardinality of the real numbers is greater than the natural numbers, he was left with a deeper question: just how large is the real line? Cantor didn’t know it yet, but our basic assumptions about the workings of mathematics are not strong enough to answer this question. This talk will explore how set theory builds up our foundation of mathematics, and how the combined work of mathematicians Kurt Gödel and Paul Cohen led to the conclusion that the Continuum Hypothesis is a statement independent of the axioms of set theory.