Event Detail

In set theory, Gödel’s program is a response to the independence phenomenon; its aim is to remove independence from set theory by passing to stronger and stronger theories of infinity that gradually decide all undecidable statements. In this talk, we will present the current state of the program and explain how it naturally leads to studying the canonical structures existing in the universe that form the core part of any foundational theory, such as Martin’s Maximum or the Axiom of Determinacy. It has also led set theorists to particularly rigid beliefs about the complexity of their guiding principles. In subsequent talks, we will examine some of these dogmas and their current status.