[PDF][PDF] Kreisel's 'shift of emphasis' and contemporary proof mining
U Kohlenbach - Studies in Logic, 2023 - studiesinlogic.sysu.edu.cn
The contemporary “proof mining” paradigm has its historical roots in Georg Kreisel's
program of “unwinding of proofs”. In this paper we elaborate on the tremendous influence …
program of “unwinding of proofs”. In this paper we elaborate on the tremendous influence …
A computational study of a class of recursive inequalities
M Neri, T Powell - arXiv preprint arXiv:2207.14559, 2022 - arxiv.org
We examine the convergence properties of sequences of nonnegative real numbers that
satisfy a particular class of recursive inequalities, from the perspective of proof theory and …
satisfy a particular class of recursive inequalities, from the perspective of proof theory and …
A finitary Kronecker's lemma and large deviations in the Strong Law of Large numbers on Banach spaces
M Neri - arXiv preprint arXiv:2411.08620, 2024 - arxiv.org
We explore the computational content of Kronecker's lemma via the proof-theoretic
perspective of proof mining and utilise the resulting finitary variant of this fundamental result …
perspective of proof mining and utilise the resulting finitary variant of this fundamental result …
Products of hyperbolic spaces
The class of uniformly smooth hyperbolic spaces was recently introduced by the first author
as a common generalization of both CAT (0) spaces and uniformly smooth Banach spaces …
as a common generalization of both CAT (0) spaces and uniformly smooth Banach spaces …
RE Bruck, proof mining and a rate of asymptotic regularity for ergodic averages in Banach spaces
A Freund, U Kohlenbach - arXiv preprint arXiv:2204.04100, 2022 - arxiv.org
We analyze a proof of Bruck to obtain an explicit rate of asymptotic regularity for Ces\aro
means in uniformly convex Banach spaces. Our rate will only depend on a norm bound and …
means in uniformly convex Banach spaces. Our rate will only depend on a norm bound and …
[PDF][PDF] The influence of the work of RE Bruck on the development of proof mining
U Kohlenbach - cms-math.net.technion.ac.il
During (mainly) the last 20 years method from mathematical logic (proof theory) were used
to obtain numerous new quantitative results as well as qualitative uniformity results in …
to obtain numerous new quantitative results as well as qualitative uniformity results in …