Mining ultraproduct proofs for bounds in polynomial rings

Thursday, November 9, 2017 - 12:00
427 Thackeray Hall
Speaker Information
William Simmons
University of Pennsylvania

Abstract or Additional Information

Ultraproducts give existence of objects without explicitly constructing them. We show how "proof mining" techniques from logic can extract uniform bounds on decision problems in polynomial and differential polynomial rings. To illustrate, we focus on the detection of prime ideals in polynomial rings over fields. We also consider proof mining of modified ultraproducts in order to obtain more precise bounds on the prime ideal problem.