Reverse mathematics and Peano categoricity

DOI10.1016/j.apal.2012.10.014zbMath1267.03030OpenAlexW2066300600MaRDI QIDQ1935867

Stephen G. Simpson, Keita Yokoyama

Publication date: 19 February 2013

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2012.10.014

zbMATH Keywords

RCAproof theoryinductive systemreverse mathematicssecond-order logicfoundations of mathematicsWKLsecond-order arithmeticlinear orderingDedekindPeano systemADS

Mathematics Subject Classification ID

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

Related Items (11)

Reverse mathematical bounds for the termination theorem ⋮ Primitive recursive reverse mathematics ⋮ Internal categoricity, truth and determinacy ⋮ HOW STRONG IS RAMSEY’S THEOREM IF INFINITY CAN BE WEAK? ⋮ Baire categoricity and \(\Sigma_1^0\)-induction ⋮ Categorical characterizations of the natural numbers require primitive recursion ⋮ Weaker cousins of Ramsey's theorem over a weak base theory ⋮ On the strength of Ramsey's theorem without Σ₁‐induction ⋮ THE BOREL COMPLEXITY OF ISOMORPHISM FOR O-MINIMAL THEORIES ⋮ REVERSE MATHEMATICS, YOUNG DIAGRAMS, AND THE ASCENDING CHAIN CONDITION ⋮ Internal categoricity in arithmetic and set theory

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