From Bolzano‐Weierstraß to Arzelà‐Ascoli

DOI10.1002/malq.201200076zbMath1331.03016arXiv1205.5429OpenAlexW3123382730MaRDI QIDQ5419209

Alexander P. Kreuzer

Publication date: 6 June 2014

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

Full work available at URL: https://arxiv.org/abs/1205.5429

zbMATH Keywords

reverse mathematicscomputabilityWKLcomputable analysisArzela-Ascoli theoremCOHBolzano-Weierstrass theoremuniform equicontinuityinstance-wise equivalencestrong cohesive principle

Mathematics Subject Classification ID

Constructive and recursive analysis (03F60) Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35) Other degrees and reducibilities in computability and recursion theory (03D30)

Cites Work

• The Bolzano-Weierstrass theorem is the jump of weak Kőnig's lemma
• \(\varPi^1_1\)-conservation of combinatorial principles weaker than Ramsey's theorem for pairs
• Sequences of real functions on [0,1 in constructive reverse mathematics]
• Things that can and things that cannot be done in PRA
• On the strength of Ramsey's theorem for pairs
• Term extraction and Ramsey's theorem for pairs
• The cohesive principle and the Bolzano-Weierstraß principle
• Effective Choice and Boundedness Principles in Computable Analysis
• Which set existence axioms are needed to prove the Cauchy/Peano theorem for ordinary differential equations?

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