Goodstein sequences for prominent ordinals up to the Bachmann-Howard ordinal

DOI10.1016/J.APAL.2011.11.006zbMath1251.03069OpenAlexW2044196525MaRDI QIDQ408160

Michiel De Smet, Andreas Weiermann

Publication date: 29 March 2012

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.2011.11.006

zbMATH Keywords

unprovabilityBachmann-Howard ordinalGoodstein sequence

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Recursive functions and relations, subrecursive hierarchies (03D20) Recursive ordinals and ordinal notations (03F15)

Related Items (1)

Mathematical logic: proof theory, constructive mathematics. Abstracts from the workshop held November 5--11, 2017

Cites Work

• Some uses of dilators in combinatorial problems. III: Independence results by means of decreasing F-sequences (F weakly finite dilator)
• Elementary descent recursion and proof theory
• Some interesting connections between the slow growing hierarchy and the Ackermann function
• The slow-growing and the Graegorczyk hierarchies
• Accessible Independence Results for Peano Arithmetic
• A Short Proof of Two Recently Discovered Independence Results Using Recursion Theoretic Methods
• 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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