I gave a talk for the Florida Atlantic University math colloquium last Friday, October 25. The abstract is below. Markus Schmidmeier, the colloquium organizer, told me today that a record number of his students attended this talk as compared to other colloquium talks, and that they told him they enjoyed the talk. It was a fun talk to give, very high-level with no proofs, an overview of set theory to encourage students to learn about it more deeply later. I touched on the ZFC axioms, forcing, inner models, and large cardinals.

Abstract: The ZFC axioms are the basic axioms underlying almost work in contemporary mathematics. Set theorists refer to the universe of all sets as V. The sets of V, as a whole, satisfy the ZFC axioms. But is this the only universe of sets? Are there other universes of sets that also satisfy the ZFC axioms? In fact, there are. I will discuss these universes of sets and how set theorists build them. I will also discuss how a statement can be true in one universe of sets but false in another. In this case, we say that the statement is independent of ZFC.