Keyword

reverse mathematics

Description: A branch of mathematical logic that studies which axioms are necessary to prove particular mathematical theorems.

Primary topic: Computability, Logic, AI Algorithms (49%)

Wikidata ID: wiki/Q2005236

OpenAlex ID: keywords/reverse-mathematics

Information theory and statistics

1959 · Journal of the Franklin Institute · 7,246

Subsystems of Second Order Arithmetic

2009 · Stephen G. Simpson · Cambridge University Press eBooks · 593

On the strength of Ramsey's theorem for pairs

2001 · Peter A. Cholak, Carl G. Jockusch, et al. · Journal of Symbolic Logic · 204

Fundamental aspects of reactor shielding

1959 · Journal of the Franklin Institute · 198

Combinatorial principles weaker than Ramsey's Theorem for pairs

2007 · Denis R. Hirschfeldt, Richard A. Shore · Journal of Symbolic Logic · 143

Effective Choice and Boundedness Principles in Computable Analysis

2011 · Vasco Brattka, Guido Gherardi · Bulletin of Symbolic Logic · 117

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On the Strength of Ramsey's Theorem

1995 · David Seetapun, Theodore A. Slaman · Notre Dame Journal of Formal Logic · 110

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Nonprovability of Certain Combinatorial Properties of Finite Trees

1985 · Stephen G. Simpson · Studies in logic and the foundations of mathematics · 110

Open Questions in Reverse Mathematics

2011 · Antonio Montalbán · Bulletin of Symbolic Logic · 97

Ordinal numbers and the Hilbert basis theorem

1988 · Stephen G. Simpson · Journal of Symbolic Logic · 86

Consistency Proofs of Subsystems of Classical Analysis

1967 · Gaisi Takeuti · Annals of Mathematics · 84

On uniform relationships between combinatorial problems

2016 · Dorias, FG, Dzhafarov, DD, et al. · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · 83

Weihrauch Complexity in Computable Analysis

2021 · Vasco Brattka, Guido Gherardi, et al. · Theory and applications of computability · 74

Mass Problems and Randomness

2005 · Stephen G. Simpson · Bulletin of Symbolic Logic · 68

Proof Theory of Impredicative Subsystems of Analysis

1988 · Wilfried Buchholz, Kurt Schütte · Medical Entomology and Zoology · 65

RT 2 2 does not imply WKL 0

2012 · Jiayi Liu · Journal of Symbolic Logic · 64

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Subsystems of Set Theory and Second Order Number Theory

1998 · Wolfram Pohlers · Studies in logic and the foundations of mathematics · 63

Measure theory and weak König's lemma

1990 · Xiaokang Yu, Stephen G. Simpson · Archive for Mathematical Logic · 63

How Incomputable Is the Separable Hahn-Banach Theorem?

2009 · Guido Gherardi, Alberto Marcone · Notre Dame Journal of Formal Logic · 62

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The metamathematics of Stable Ramsey’s Theorem for Pairs

2014 · C. T. Chong, Theodore A. Slaman, et al. · Journal of the American Mathematical Society · 60

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The limits of determinacy in second-order arithmetic

2011 · Antonio Montalbán, Richard A. Shore · Proceedings of the London Mathematical Society · 60

The atomic model theorem and type omitting

2009 · Denis R. Hirschfeldt, Richard A. Shore, et al. · Transactions of the American Mathematical Society · 60

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On the (semi)lattices induced by continuous reducibilities

2012 · Arno Pauly · 58

Higher Order Reverse Mathematics

2000 · Ulrich Kohlenbach · BRICS Report Series · 57

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Reverse mathematics and ordinal exponentiation

1994 · Jeffry L. Hirst · Annals of Pure and Applied Logic · 53

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Works count: 1,741

Citation count: 17,040