A WALK WITH GOODSTEIN

DOI10.1017/bsl.2024.1arXiv2004.09110MaRDI QIDQ6204143

Andreas Weiermann, David Fernández-Duque

Publication date: 9 April 2024

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

Full work available at URL: https://arxiv.org/abs/2004.09110

zbMATH Keywords

fast-growing functionsGoodstein's theoremproofs of independence

Mathematics Subject Classification ID

Recursive functions and relations, subrecursive hierarchies (03D20) Computability and recursion theory on ordinals, admissible sets, etc. (03D60) Gödel numberings and issues of incompleteness (03F40)

Cites Work

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• On Gödel incompleteness and finite combinatorics
• Two further combinatorial theorems equivalent to the 1-consistency of peano arithmetic
• Classifying the Provably Total Functions of PA
• Combinatorial principles concerning approximations of functions
• Flipping properties in arithmetic
• Accessible Independence Results for Peano Arithmetic
• An Unprovable Ramsey-Type Theorem
• Built-up systems of fundamental sequences and hierarchies of number-theoretic functions
• A Uniform Approach to Fundamental Sequences and Hierarchies
• A Short Proof of Two Recently Discovered Independence Results Using Recursion Theoretic Methods
• Predicatively unprovable termination of the Ackermannian Goodstein process
• Goodstein’s Theorem Revisited
• Classifying Phase Transition Thresholds for Goodstein Sequences and Hydra Games
• Transfinite ordinals in recursive number theory
• On the restricted ordinal theorem

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