Patterns of resemblance of order 2

DOI10.1016/J.APAL.2008.10.006zbMath1206.03050OpenAlexW1987053402MaRDI QIDQ1011757

Timothy J. Carlson

Publication date: 9 April 2009

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

Full work available at URL: https://doi.org/10.1016/j.apal.2008.10.006

zbMATH Keywords

proof theoryreflection principlesnatural well-orderingsordinal notation systems\(\Sigma_n\)-elementary substructurespatterns resemblance

Mathematics Subject Classification ID

Large cardinals (03E55) Recursive ordinals and ordinal notations (03F15) Ordinal and cardinal numbers (03E10)

Related Items (9)

Open Questions in Reverse Mathematics ⋮ Pure patterns of order 2 ⋮ Tracking chains of \(\varSigma_2\)-elementarity ⋮ Normal forms for elementary patterns ⋮ Ordinal arithmetic with simultaneously defined theta-functions ⋮ Arithmetical algorithms for elementary patterns ⋮ Generalizing Kruskal's theorem to pairs of cohabitating trees ⋮ Pure \(\Sigma_2\)-elementarity beyond the core ⋮ A Glimpse of $$ \sum_{3} $$-elementarity

Cites Work

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• \(\Sigma _{1}\)-elementarity and Skolem hull operators
• Proof theory. 2nd ed
• Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies
• Knowledge, machines, and the consistency of Reinhardt's strong mechanistic thesis
• Ordinal arithmetic and \(\Sigma_1\)-elementarity
• Models of axiomatic theories admitting automorphisms
• Assignment of ordinals to patterns of resemblance
• Some applications of model theory in set theory
• Elementary patterns of resemblance

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