The logical complexity of Schanuel’s Conjecture
University of Illinois at Chicago
In its most natural form Schanuel’s Conjecture is a $\Pi_1^1$-statement. We will show that there is an equivalent $\Pi^0_3$-statement. They key idea is a result of Jonathan Kirby showing that, if Schanuel’s Conjecture is false, then there are canonical counterexamples. Most of my lecture will describe Kirby’s work.
Professor Marker holds the position of LAS Distinguished Professor in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago. He conducts research in model theory and it applications, particularly in applications to real algebraic geometry and real analytic geometry, exponentiation and differential algebra. His excellent textbook Model Theory: an Introduction is widely studied.