The Baire category theorem in weak subsystems of second-order arithmetic

DOI10.2307/2275219zbMath0794.03085OpenAlexW2055394931MaRDI QIDQ3138013

Stephen G. Simpson, Douglas K. Brown

Publication date: 24 October 1993

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2275219

zbMATH Keywords

functional analysisHilbert's programweak subsystems of second-order arithmeticReverse MathematicsBaire Category theorem

Mathematics Subject Classification ID

Models of arithmetic and set theory (03C62) Second- and higher-order arithmetic and fragments (03F35)

Related Items (10)

Representations and the foundations of mathematics ⋮ On the uniform computational content of the Baire category theorem ⋮ The Typical Constructible Object ⋮ On the strength of Ramsey's theorem ⋮ ALMOST THEOREMS OF HYPERARITHMETIC ANALYSIS ⋮ A measure-theoretic proof of Turing incomparability ⋮ Baire categoricity and \(\Sigma_1^0\)-induction ⋮ Forcing in Proof Theory ⋮ Formalizing forcing arguments in subsystems of second-order arithmetic ⋮ Some conservation results on weak König's lemma

Cites Work

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• Fragments of arithmetic
• Weak comparability of well orderings and reverse mathematics
• Countable algebra and set existence axioms
• Factorization of polynomials and \(\Sigma ^ 0_ 1\) induction
• Which set existence axioms are needed to prove the separable Hahn-Banach theorem?
• Which set existence axioms are needed to prove the Cauchy/Peano theorem for ordinary differential equations?
• Class groups of integral group rings

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