Systems of iterated projective ordinal notations and combinatorial statements about binary labeled trees

DOI10.1007/BF01630809zbMath0691.03039OpenAlexW2065310207MaRDI QIDQ582289

L. N. Gordeev

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1007/bf01630809

zbMATH Keywords

reverse mathematicswell-quasi-orderingbinary treeswell-orderingD-functionsiterated inductive definitionsiterated projective ordinal notationslabelled treesVeblen-Bachmann-hierarchy

Mathematics Subject Classification ID

Recursive ordinals and ordinal notations (03F15)

Related Items (5)

Investigations on slow versus fast growing: How to majorize slow growing functions nontrivially by fast growing ones ⋮ How to Compare Buchholz-Style Ordinal Notation Systems with Gordeev-Style Notation Systems ⋮ Ordinal notation systems corresponding to Friedman's linearized well-partial-orders with gap-condition ⋮ Strong WQO Tree Theorems ⋮ Ordinal arithmetic with simultaneously defined theta-functions

Cites Work

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• Proof theory. 2nd ed
• An independence result for \((\Pi^ 1_ 1-CA)+BI\)
• Eine Erweiterung T(V') des Ordinalzahlensystems \(C_{\Omega}(\Lambda _ 0)\) von G. Jäger. (An extension T(V') of the ordinal system \(C_{\Omega}(\Lambda _ 0)\) by G. Jäger)
• A new system of proof-theoretic ordinal functions
• Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies
• ϱ-inaccessible ordinals, collapsing functions and a recursive notation system
• Majorisier Ungsrelationen und Fundamentalfolgen eines Ordinalzahlensystems von G. Jäger
• Generalizations of the one-dimensional version of the Kruskal-Friedman theorems

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