HOW STRONG IS RAMSEY’S THEOREM IF INFINITY CAN BE WEAK?

DOI10.1017/jsl.2022.46arXiv2011.02550OpenAlexW3096193878WikidataQ113858276 ScholiaQ113858276MaRDI QIDQ6103456

Katarzyna W. Kowalik, Leszek Aleksander Kołodziejczyk, Keita Yokoyama

Publication date: 5 June 2023

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

Full work available at URL: https://arxiv.org/abs/2011.02550

zbMATH Keywords

automorphismsnonstandard modelsreverse mathematicsRamsey's theoremfirst-order arithmeticdefinable cutsproof speedup

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Foundations of classical theories (including reverse mathematics) (03B30) Ramsey theory (05D10) Nonstandard models of arithmetic (03H15) Second- and higher-order arithmetic and fragments (03F35)

Related Items (1)

Primitive recursive reverse mathematics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Categorical characterizations of the natural numbers require primitive recursion
• The inductive strength of Ramsey's theorem for pairs
• The degree of a \(\Sigma_ n\) cut
• Factorization of polynomials and \(\Sigma ^ 0_ 1\) induction
• The proof-theoretic strength of Ramsey's theorem for pairs and two colors
• On the strength of Ramsey's theorem
• Reverse mathematics and Peano categoricity
• Some upper bounds on ordinal-valued Ramsey numbers for colourings of pairs
• Weaker cousins of Ramsey's theorem over a weak base theory
• Unifying the model theory of first-order and second-order arithmetic via \(\mathrm{WKL}_0^\ast\)
• Algebraic disguises of \(\Sigma ^ 0_ 1\) induction
• On the strength of Ramsey's theorem for pairs
• The metamathematics of Stable Ramsey’s Theorem for Pairs
• A Correction to "On Extensions of Models of Strong Fragments of Arithmetic"
• Reflection principles and provability algebras in formal arithmetic
• The Pigeonhole Principle and Fragments of Arithmetic
• On elementary cuts in recursively saturated models of Peano Arithmetic
• Model-theoretic properties characterizing Peano arithmetic
• On Extensions of Models of Strong Fragments of Arithmetic
• Constructing κ-like Models of Arithmetic
• On the strength of Ramsey's theorem without Σ₁‐induction
• Random reals, the rainbow Ramsey theorem, and arithmetic conservation
• Where pigeonhole principles meet Koenig lemmas
• Ramsey's theorem and recursion theory

This page was built for publication: HOW STRONG IS RAMSEY’S THEOREM IF INFINITY CAN BE WEAK?