Vopenka's Principle: a useful strong axiom
Time and place
1 PM on Tuesday, November 16th, 2010; NAC 6-113
Andrew Brooke-Taylor (University of Bristol)
Abstract
Vopenka's Principle is an axiom that can be added to the usual system of axioms for mathematics to give significantly more strength. It was used quite recently to resolve an important open question in algebraic topology: assuming Vopenka's Principle, localisation functors exist for all generalised cohomology theories. After describing the axiom and sketching this application, I will talk about some recent results showing that Vopenka's Principle is compatible (to be precise, relatively consistent) with a wide range of other statements known to be independent of the usual set theory axioms. The proof is by showing that it is unaffected by many forcing constructions, which are the standard technique for proving independence results.
