How the Schanuel and Andre Conjectures Affect Logical Questions About the Real and Complex Exponentials and the Weierstrass Elliptic Functions

SPECIAL LOGIC/NUMBER THEORY
Topic:How the Schanuel and Andre Conjectures Affect Logical Questions About the Real and Complex Exponentials and the Weierstrass Elliptic Functions
Speaker:A. MacIntyre
Affiliation:London University
Date:Tuesday, September 25
Time/Room:4:00pm - 5:00pm/S-101

The logical questions concern algorithms for testing solvability of equations (and more generally truth of first-order sentences), and have positive answers for the real exponential and the Weierstrass functions (assuming respectively the Schanuel and Andre Conjectures). For the complex exponential the answers are negative, but there insights of Zilber around the model theory of Schanuel's Conjecture lead to new ideas on which exponential equations can be solved in the complex field.