Logic Seminar

William SimmonsHobart and William Smith Colleges
Mining for bounds: Ultraproducts, proof transformations, and effective algebra.

Tuesday, December 3, 2019 - 2:55pm
Malott 206

We show how "proof mining" techniques from logic can extract concrete information from abstract proofs, even those involving nonconstructive objects like ultraproducts. We focus on uniform bounds in polynomial rings. Our central results are an explicit polynomial-growth bound on prime ideals in polynomial rings over fields and a related bound in differential algebra.