Journal
ADVANCES IN MATHEMATICS
Volume 343, Issue -, Pages 567-623Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2018.11.026
Keywords
Proof mining; Functional interpretation; Differential algebra; Uniform bounds; Ultraproduct
Categories
Funding
- NSF [DMS-1600263]
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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. (C) 2018 Elsevier Inc. All rights reserved.
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