Derivatives of normal functions in reverse mathematics

DOI10.1016/j.apal.2020.102890zbMath1473.03036arXiv1904.04630OpenAlexW2940438007MaRDI QIDQ2216034

Anton Freund, Michael Rathjen

Publication date: 15 December 2020

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.04630

zbMATH Keywords

derivativesordinal notationsreverse mathematicsbar inductionwell-ordering principlesdilatorsnormal functions (on the ordinals)

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)

Related Items (9)

Minimal bad sequences are necessary for a uniform Kruskal theorem ⋮ Boundedness theorems for flowers and sharps ⋮ Well ordering principles for iterated \(\Pi^1_1\)-comprehension ⋮ PREDICATIVE COLLAPSING PRINCIPLES ⋮ HOW STRONG ARE SINGLE FIXED POINTS OF NORMAL FUNCTIONS? ⋮ WELL ORDERING PRINCIPLES AND -STATEMENTS: A PILOT STUDY ⋮ Patterns of resemblance and Bachmann-Howard fixed points ⋮ From Kruskal’s theorem to Friedman’s gap condition ⋮ Reflecting and unfolding

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Proof-theoretic investigations on Kruskal's theorem
• Derivatives of normal functions and \(\omega \)-models
• \(\Pi_1^1\)-comprehension as a well-ordering principle
• Introduction to \(\Pi^1_2\)-logic
• The Veblen functions for computability theorists
• On the relation between choice and comprehension principles in second order arithmetic
• Π12-logic, Part 1: Dilators
• Computable aspects of the Bachmann–Howard principle
• A categorical construction of Bachmann–Howard fixed points
• Systems of predicative analysis
• Eine Grenze Für die Beweisbarkeit der Transfiniten Induktion in der Verzweigten Typenlogik
• A note on ordinal exponentiation and derivatives of normal functions

This page was built for publication: Derivatives of normal functions in reverse mathematics