Benjamin Siskind

The inner model program

The standard axiom system for mathematics, ZFC, doesn't decide many natural statements about sets. For example, Cantor's Continuum Hypothesis (CH), which asserts that there is no set with size strictly between the size of the natural numbers and the size of the real numbers, is independent of ZFC. Gödel proposed that we should seek out justified new axioms to add to ZFC in order to decide natural independent statements, like CH. He proposed that such new axioms might only be extrinsically justified, as evidenced by their role in the landscape of natural extensions of ZFC. In this talk, we will give an overview of an area of research which is fundamental to understanding this landscape: inner model theory.