Baire categoricity and \(\Sigma_1^0\)-induction

DOI10.1215/00294527-2377887zbMath1331.03017OpenAlexW2069846627MaRDI QIDQ2443120

Stephen G. Simpson

Publication date: 4 April 2014

Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ndjfl/1390246439

zbMATH Keywords

BCTRCAreverse mathematicsEFAsecond-order arithmeticBaire category theorem\(\mathsf{RCA} _{0}^{\ast}\)\(\mathsf{RCA}_{0}\)\(\Sigma^{0}_{1}\)-induction

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35) Relative consistency and interpretations (03F25)

Related Items (4)

On the uniform computational content of the Baire category theorem ⋮ Primitive recursive reverse mathematics ⋮ THE BOREL COMPLEXITY OF ISOMORPHISM FOR O-MINIMAL THEORIES ⋮ REVERSE MATHEMATICS, YOUNG DIAGRAMS, AND THE ASCENDING CHAIN CONDITION

Cites Work

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• Fragments of arithmetic
• Factorization of polynomials and \(\Sigma ^ 0_ 1\) induction
• Some conservation results on weak König's lemma
• Reverse mathematics and Peano categoricity
• The Baire category theorem in weak subsystems of second-order arithmetic
• The atomic model theorem and type omitting
• On the strength of Ramsey's theorem without Σ₁‐induction
• Some More Conservation Results on the Baire Category Theorem

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