On the strength of Ramsey's theorem without Σ1‐induction

DOI10.1002/malq.201200047zbMath1267.03031OpenAlexW2097268843MaRDI QIDQ4915224

Keita Yokoyama

Publication date: 9 April 2013

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

Full work available at URL: https://doi.org/10.1002/malq.201200047

zbMATH Keywords

RCAindicator functionreverse mathematicsproof-theoretic strengthconservationRamsey's theoremWKLEFA

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Ramsey theory (05D10) Second- and higher-order arithmetic and fragments (03F35)

Related Items (11)

The proof-theoretic strength of Ramsey's theorem for pairs and two colors ⋮ Nonstandard second-order arithmetic and Riemann's mapping theorem ⋮ Primitive recursive reverse mathematics ⋮ HOW STRONG IS RAMSEY’S THEOREM IF INFINITY CAN BE WEAK? ⋮ The Paris-Harrington principle and second-order arithmetic -- bridging the finite and infinite Ramsey theorem ⋮ Baire categoricity and \(\Sigma_1^0\)-induction ⋮ Algebraic combinatorics in bounded induction ⋮ Weaker cousins of Ramsey's theorem over a weak base theory ⋮ THE BOREL COMPLEXITY OF ISOMORPHISM FOR O-MINIMAL THEORIES ⋮ REVERSE MATHEMATICS, YOUNG DIAGRAMS, AND THE ASCENDING CHAIN CONDITION ⋮ In search of the first-order part of Ramsey's theorem for pairs

Cites Work

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• \(\varPi^1_1\)-conservation of combinatorial principles weaker than Ramsey's theorem for pairs
• Factorization of polynomials and \(\Sigma ^ 0_ 1\) induction
• Reverse mathematics and Peano categoricity
• The strength of infinitary Ramseyan principles can be accessed by their densities
• On the strength of Ramsey's theorem for pairs
• Some independence results for Peano arithmetic

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