Elementary patterns of resemblance

DOI10.1016/S0168-0072(00)00040-3zbMath1009.03026MaRDI QIDQ5935985

Timothy J. Carlson

Publication date: 22 April 2003

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

zbMATH Keywords

proof theory\(\Pi^1_2\)-logiccore model theoryKripke-Platek set theoryordinal arithmeticordinal notationspartial ordering on the class of ordinalsset theoryVeblen function

Mathematics Subject Classification ID

Inner models, including constructibility, ordinal definability, and core models (03E45) Proof theory in general (including proof-theoretic semantics) (03F03) Partition relations (03E02) Recursive ordinals and ordinal notations (03F15)

Related Items (17)

The Bachmann-Howard structure in terms of \(\Sigma_1\)-elementarity ⋮ Ordinal arithmetic based on Skolem hulling ⋮ \(\Sigma _{1}\)-elementarity and Skolem hull operators ⋮ Pure patterns of order 2 ⋮ Tracking chains of \(\varSigma_2\)-elementarity ⋮ A machine that knows its own code ⋮ Normal forms for elementary patterns ⋮ Ordinal arithmetic with simultaneously defined theta-functions ⋮ Arithmetical algorithms for elementary patterns ⋮ 2003 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquim '03 ⋮ Theories and ordinals in proof theory ⋮ Generalizing Kruskal's theorem to pairs of cohabitating trees ⋮ Pure \(\Sigma_2\)-elementarity beyond the core ⋮ Patterns of resemblance of order 2 ⋮ Patterns of resemblance and Bachmann-Howard fixed points ⋮ SELF-REFERENTIAL THEORIES ⋮ A Glimpse of $$ \sum_{3} $$-elementarity

Cites Work

• 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
• Recent Advances in Ordinal Analysis: Π¹₂— CA and Related Systems
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