A Uniform Approach to Fundamental Sequences and Hierarchies

DOI10.1002/malq.19940400212zbMath0812.03023OpenAlexW2115737962MaRDI QIDQ4304112

Adam Cichon, Andreas Weiermann, Wilfried Buchholz

Publication date: 14 May 1995

Published in: Mathematical Logic Quarterly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/malq.19940400212

zbMATH Keywords

normrecursive functionsHardy functionordinal notationfundamental sequencesnumber-theoretic functionHardy hierarchiesBachmann propertyKripke-Platek set theory with a recursive Mahlo ordinal

Mathematics Subject Classification ID

Recursive functions and relations, subrecursive hierarchies (03D20) Recursive ordinals and ordinal notations (03F15) Ordinal and cardinal numbers (03E10)

Related Items (31)

How is it that infinitary methods can be applied to finitary mathematics? Gödel's T: a case study ⋮ A comparison of well-known ordinal notation systems for \(\varepsilon _{0}\) ⋮ On the Performance of Axiom Systems ⋮ Investigations on slow versus fast growing: How to majorize slow growing functions nontrivially by fast growing ones ⋮ Sometimes slow growing is fast growing ⋮ The hierarchy of terminating recursive programs over N ⋮ Streamlined subrecursive degree theory ⋮ Functorial Fast-Growing Hierarchies ⋮ Predicatively unprovable termination of the Ackermannian Goodstein process ⋮ A WALK WITH GOODSTEIN ⋮ How to characterize provably total functions by local predicativity ⋮ Normal forms for elementary patterns ⋮ Phase transitions of iterated Higman-style well-partial-orderings ⋮ From Subsystems of Analysis to Subsystems of Set Theory ⋮ Termination proofs for term rewriting systems by lexicographic path orderings imply multiply recursive derivation lengths ⋮ Multiply-Recursive Upper Bounds with Higman’s Lemma ⋮ Some interesting connections between the slow growing hierarchy and the Ackermann function ⋮ A Computation of the Maximal Order Type of the Term Ordering on Finite Multisets ⋮ Accessible Recursive Functions ⋮ Ackermann's substitution method (remixed) ⋮ The Hydra battle and Cichon's principle ⋮ GOODSTEIN SEQUENCES BASED ON A PARAMETRIZED ACKERMANN–PÉTER FUNCTION ⋮ On a question of Andreas Weiermann ⋮ Iterated Inductive Definitions Revisited ⋮ Classifying the phase transition threshold for Ackermannian functions ⋮ Complexity of Gödel’s T in λ-Formulation ⋮ Analytic combinatorics, proof-theoretic ordinals, and phase transitions for independence results ⋮ Partitioning 𝛼–large sets: Some lower bounds ⋮ Classifying the Provably Total Functions of PA ⋮ Variations on a theme by Weiermann ⋮ Ackermannian Goodstein sequences of intermediate growth

Cites Work

• Unnamed Item
• P.R.-Regulated Systems of Notation and the Subrecursive Hierarchy Equivalence Property

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