Proof theory and ordinal analysis

DOI10.1007/BF01621474zbMath0724.03033OpenAlexW2026374478MaRDI QIDQ2276954

Wolfram Pohlers

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1007/bf01621474

zbMATH Keywords

Kripke-Platek set theorylarge cardinalsordinal notationsSkolem functionsordinal analysisnumber theoryHilbert's programprovably recursive functionslocal predicativitygeneralized inductive definitionsimpredicativitycollapsingsproof theoretic ordinalprovably total \(\Sigma _ 1\)-functions

Mathematics Subject Classification ID

Cut-elimination and normal-form theorems (03F05) Large cardinals (03E55) Structure of proofs (03F07) Second- and higher-order arithmetic and fragments (03F35) Proof theory in general (including proof-theoretic semantics) (03F03) Recursive ordinals and ordinal notations (03F15) Complexity of proofs (03F20)

Related Items (14)

Proof theory of reflection ⋮ The Bachmann-Howard structure in terms of \(\Sigma_1\)-elementarity ⋮ Ordinal arithmetic based on Skolem hulling ⋮ Recent Advances in Ordinal Analysis: Π¹₂— CA and Related Systems ⋮ How to characterize provably total functions by local predicativity ⋮ What's so special about Kruskal's theorem and the ordinal \(\Gamma{}_ 0\)? A survey of some results in proof theory ⋮ Pure Proof Theory Aims, Methods and Results: Extended Version of Talks Given at Oberwolfach and Haifa ⋮ Fixed points in Peano arithmetic with ordinals ⋮ An ordinal analysis of stability ⋮ An ordinal analysis of parameter free \(\Pi^{1}_{2}\)-comprehension ⋮ Pure \(\Sigma_2\)-elementarity beyond the core ⋮ A Glimpse of $$ \sum_{3} $$-elementarity ⋮ Proof-theoretic analysis of KPM ⋮ Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM

Cites Work

• Proof-theoretic analysis of KPM
• Ordinal notations based on a weakly Mahlo cardinal
• Proof theory. 2nd ed
• A new system of proof-theoretic ordinal functions
• Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies
• Elementary induction on abstract structures
• Proof theory. An introduction
• Notation systems for infinitary derivations
• Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie
• ϱ-inaccessible ordinals, collapsing functions and a recursive notation system
• The slow-growing and the Graegorczyk hierarchies
• Π12-logic, Part 1: Dilators
• Systems of predicative analysis
• Eine Grenze Für die Beweisbarkeit der Transfiniten Induktion in der Verzweigten Typenlogik
• Hierarchies of number-theoretic functions. I
• A classification of the ordinal recursive functions
• Ordinal recursion, and a refinement of the extended Grzegorczyk hierarchy
• The consistency of arithmetics
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