Graduate Pizza Seminar
Can we quantify the strength of a theorem?
Juan Aguilera, Rutgers University
Location: Hill GSL
Date & time: Friday, 01 December 2017 at 1:40PM - 2:40PM
|ABSTRACT: Ordinal analysis is a part of logic that deals with assigning numbers to theorems (or collections of theorems) as a measure of their strength. In practice, a theorem to which we have assigned a large number has many consequences, and, in many natural cases, if a theorem A has a smaller number associated to it than B, then B implies A. For example, the Bolzano-Weierstrass theorem implies (in a meaningful way) that every countable field has a unique algebraic closure.