Provable wellorderings of formal theories for transfinitely iterated inductive definitions

DOI10.2307/2271954zbMath0411.03046OpenAlexW4239786980MaRDI QIDQ4198748

Wilfried Buchholz, Wolfram Pohlers

Publication date: 1978

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

Full work available at URL: http://nbn-resolving.de/urn:nbn:de:bvb:19-epub-3838-9

zbMATH Keywords

proof-theoretic strengthproof-theoretic ordinalfirst order arithmeticprovable well-orderings of formal theoriestransfinitely iterated inductive definitions

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Recursive ordinals and ordinal notations (03F15)

Related Items (15)

Zur Beweistheorie Der Kripke-Platek-Mengenlehre Über Den Natürlichen Zahlen ⋮ Simplified Cut Elimination for Kripke-Platek Set Theory ⋮ A new system of proof-theoretic ordinal functions ⋮ A proof-theoretic account of classical principles of truth ⋮ Beweistheoretische Abgrenzung von Teilsystemen der Analysis ⋮ Natural well-orderings ⋮ Well-Partial Orderings and their Maximal Order Types ⋮ Choice principles, the bar rule and autonomously iterated comprehension schemes in analysis ⋮ Notes on some second-order systems of iterated inductive definitions and \(\Pi_1^1\)-comprehensions and relevant subsystems of set theory ⋮ Ordinals connected with formal theories for transfinitely iterated inductive definitions ⋮ Iterated Inductive Definitions Revisited ⋮ Replacement versus collection and related topics in constructive Zermelo-Fraenkel set theory ⋮ A well-ordering proof for Feferman's theoryT 0 ⋮ Cut-elimination for impredicative infinitary systems part I. Ordinal-analysis for ID1 ⋮ Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM

Cites Work

• On ordinal diagrams
• Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie
• A simplification of the Bachmann method for generating large countable ordinals
• Die Beziehungen Zwischen den OrdinalzahlsystemenΣ Und $$\bar \Theta \left( \omega \right)$$
• Ein konstruktives system von Ordinalzahlen
• Ein Bezeichnungssystem für Ordinalzahlen
• Ein Bezeichnungssystem für Ordinalzahlen
• A system of abstract constructive ordinals

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