Proof-theoretic uniform boundedness and bounded collection principles and countable Heine-Borel compactness

DOI10.1007/s00153-021-00771-wzbMath1487.03065OpenAlexW3159871748MaRDI QIDQ2238150

Ulrich Kohlenbach

Publication date: 29 October 2021

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00153-021-00771-w

zbMATH Keywords

uniform boundedness principleproof miningmonotone functional interpretationbounded functional interpretationbounded collection principle

Mathematics Subject Classification ID

Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Functionals in proof theory (03F10)

Related Items

On false Heine/Borel compactness principles in proof mining

Cites Work

• Unnamed Item
• Unnamed Item
• On quantitative versions of theorems due to F. E. Browder and R. Wittmann
• An example concerning fixed points
• Mann iterates of directionally nonexpansive mappings in hyperbolic spaces
• Moduli of regularity and rates of convergence for Fejér monotone sequences
• On the removal of weak compactness arguments in proof mining
• Bounded functional interpretation
• Iteration processes for nonexpansive mappings
• Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space
• Some logical metatheorems with applications in functional analysis
• A Logical Uniform Boundedness Principle for Abstract Metric and Hyperbolic Spaces
• On the reverse mathematics and Weihrauch complexity of moduli of regularity and uniqueness
• General logical metatheorems for functional analysis
• Applied Proof Theory: Proof Interpretations and Their Use in Mathematics