Proof mining and effective bounds in differential polynomial rings
Logic
2018-10-17 v2 Commutative Algebra
Abstract
Using the functional interpretation from proof theory, we analyze nonconstructive proofs of several central theorems about polynomial and differential polynomial rings. We extract effective bounds, some of which are new to the literature, from the resulting proofs. In the process we discuss the constructive content of Noetherian rings and the Nullstellensatz in both the classical and differential settings. Sufficient background is given to understand the proof-theoretic and differential-algebraic framework of the main results.
Cite
@article{arxiv.1609.07509,
title = {Proof mining and effective bounds in differential polynomial rings},
author = {William Simmons and Henry Towsner},
journal= {arXiv preprint arXiv:1609.07509},
year = {2018}
}