Independence of Ramsey theorem variants using $\varepsilon _0$

DOI10.1090/proc12759zbMath1402.03083OpenAlexW1488002935MaRDI QIDQ2789881

Harvey M. Friedman, Florian Pelupessy

Publication date: 2 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc12759

zbMATH Keywords

independenceRamsey theoryPeano arithmeticParis-HarringtonunprovabilityHardy hierarchyfundamental sequencesCantor normal formfinite adjacent Ramsey theoremhydra battles

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Generalized Ramsey theory (05C55) Ramsey theory (05D10) Recursive functions and relations, subrecursive hierarchies (03D20) Recursive ordinals and ordinal notations (03F15)

Related Items (6)

Phase transition results for three Ramsey-like theorems ⋮ Partial Orders and Immunity in Reverse Mathematics ⋮ Monomial ideals and independence of ⋮ Reverse mathematics of the finite downwards closed subsets of ordered by inclusion and adjacent Ramsey for fixed dimension ⋮ Predicatively unprovable termination of the Ackermannian Goodstein process ⋮ Dickson's lemma and weak Ramsey theory

Cites Work

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• Rapidly growing Ramsey functions
• Handbook of proof theory
• Proof theory. An introduction
• The Hydra Battle Revisited
• Accessible Independence Results for Peano Arithmetic
• An Unprovable Ramsey-Type Theorem
• A Short Proof of Two Recently Discovered Independence Results Using Recursion Theoretic Methods

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