Rethinking set theory
Tom Leinster (U Glasgow)
Wednesday 21st April, 2010 16:00-17:00 204
At the heart of mathematical culture is a niggling worry. We use basic set-theoretic language all the time, and we are informed that ZFC is the "foundation of mathematics". Yet most of us sail through life neither knowing nor much caring what the axioms of ZFC are; and if we do stop to look at the axioms, they seem curiously remote from what we as mathematicians actually do. I will present a solution to this problem, due to Lawvere. It is a radical reshaping of set theory. The axioms are 10 totally mundane properties of sets, used every day by ordinary mathematicians. In this way, I hope to persuade you that set theory is not to be sniffed at.