The cohesive principle and the Bolzano-Weierstraß principle

DOI10.1002/MALQ.201010008zbMath1243.03016arXiv1005.5316OpenAlexW3124326917MaRDI QIDQ3008059

Alexander P. Kreuzer

Publication date: 17 June 2011

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

Full work available at URL: https://arxiv.org/abs/1005.5316

zbMATH Keywords

reverse mathematicsBolzano-Weierstrass principlecohesive principle

Mathematics Subject Classification ID

Constructive and recursive analysis (03F60) Foundations of classical theories (including reverse mathematics) (03B30) Computation over the reals, computable analysis (03D78)

Related Items (6)

Term extraction and Ramsey's theorem for pairs ⋮ The Bolzano-Weierstrass theorem is the jump of weak Kőnig's lemma ⋮ On the uniform computational content of computability theory ⋮ Primitive recursion and the chain antichain principle ⋮ From Bolzano‐Weierstraß to Arzelà‐Ascoli ⋮ Nets and reverse mathematics

Cites Work

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• Things that can and things that cannot be done in PRA
• On the strength of Ramsey's theorem for pairs
• On the computational content of the Bolzano-Weierstraß Principle
• Combinatorial principles weaker than Ramsey's Theorem for pairs
• Singular coverings and non‐uniform notions of closed set computability
• Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space
• A cohesive set which is not high
• Applied Proof Theory: Proof Interpretations and Their Use in Mathematics

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