Sat Dec 4, 2010
60 Evans Hall, 12:10–2 AM
John R. Steel (Professor of Mathematics, University of California, Berkeley)
The Triple Helix
Many different foundational theories have been developed and studied by set theorists. Remarkably, no divergence at the level of statements about “concrete” objects (for example, natural numbers) has emerged, and indeed, these theories are linearly ordered by the inclusion order on their sets of arithmetic consequences. The place of a theory in this order is known as its consistency strength.
Our methods for comparing the consistency strengths of set theories center on three intertwined canonical hierarchies of sets. In this talk we shall describe those three hierarchies in very general terms. We shall focus on the philosophical significance of the results and open questions concerning them.
The biweekly LOGIC TEA will be held in the Alfred Tarski Room (727 Evans Hall) immediately following the Colloquium (with support from the Graduate Assembly).