Well ordering principles for iterated \(\Pi^1_1\)-comprehension

DOI10.1007/s00029-023-00879-2arXiv2112.08005MaRDI QIDQ6080077

Anton Freund, Michael Rathjen

Publication date: 30 October 2023

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.08005

zbMATH Keywords

reverse mathematicsordinal analysisadmissible setstransfinite recursiondilatorswell ordering principlesiterated \(\Pi^1_1\)-comprehensionordinal collapsing functions

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35) Recursive ordinals and ordinal notations (03F15) Ordinal and cardinal numbers (03E10) Computability and recursion theory on ordinals, admissible sets, etc. (03D60)

Cites Work

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• Proof theory. The first step into impredicativity
• Reverse mathematics and well-ordering principles: a pilot study
• A new system of proof-theoretic ordinal functions
• The Galvin-Prikry theorem and set existence axioms
• Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies
• Proof-theoretic investigations on Kruskal's theorem
• Bar induction and \(\omega\) model reflection
• Reverse mathematics and ordinal exponentiation
• Well-quasiordering finite trees with gap-condition. Proof of Harvey Friedman's conjecture
• Patterns of resemblance and Bachmann-Howard fixed points
• Minimal bad sequences are necessary for a uniform Kruskal theorem
• Derivatives of normal functions in reverse mathematics
• \(\Pi_1^1\)-comprehension as a well-ordering principle
• Introduction to \(\Pi^1_2\)-logic
• Gentzen's Centenary
• The Veblen functions for computability theorists
• Open Questions in Reverse Mathematics
• Ein System des Verknüpfenden Schliessens
• Weak axioms of determinacy and subsystems of analysis I: δ20 games
• Beweistheorie vonKPN
• Cut elimination for impredicative infinitary systems. Part II ordinal analysis for iterated inductive definitions
• Π12-logic, Part 1: Dilators
• Zur Beweistheorie Der Kripke-Platek-Mengenlehre Über Den Natürlichen Zahlen
• From Kruskal’s theorem to Friedman’s gap condition
• Well-ordering Principles, ω-models and $$ \varPi_{1}^{1} $$-comprehension
• Well-Ordering Principles in Proof Theory and Reverse Mathematics
• PREDICATIVE COLLAPSING PRINCIPLES
• Set-theoretic reflection is equivalent to induction over well-founded classes
• Computable aspects of the Bachmann–Howard principle
• A categorical construction of Bachmann–Howard fixed points
• Eine Grenze Für die Beweisbarkeit der Transfiniten Induktion in der Verzweigten Typenlogik
• Bachmann-Howard derivatives