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Ordinal analysis

In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength. If theories have the same proof-theoretic ordinal they are often equiconsistent, and if one theory has a larger proof-theoretic ordinal than another it can often prove the consistency of the second theory.

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Table of ordinal analyses

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Ordinal analysis

Nodes66
Edges65
Triples16
Avg. degree1.97
Density0.030303
Components1

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Ordinal analysis

Top relations

related to Ordinal notations · 8
Ordinal analysis → For, However, Including, PA, PTO, Rathjen, Some, Z2
related to Definition · 4
Ordinal analysis → Equivalently, Kleene's, Ordinal, The
related to history · 4
Ordinal analysis → Gerhard Gentzen, Peano, See Gentzen's, The

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displaystyle mathsf theory ordinal arithmetic type induction proof-theoretic axiom w-types set recursive universe omega theories pa augmented iterated kpi used

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SubjectPredicateObjectConfidenceSrc
Ordinal analysisrelated to DefinitionOrdinal0.60section
Ordinal analysisrelated to DefinitionThe0.60section
Ordinal analysisrelated to DefinitionKleene's0.60section
Ordinal analysisrelated to DefinitionEquivalently0.60section
Ordinal analysisrelated to historyThe0.60section
Ordinal analysisrelated to historyGerhard Gentzen0.60section
Ordinal analysisrelated to historyPeano0.60section
Ordinal analysisrelated to historySee Gentzen's0.60section
Ordinal analysisrelated to Ordinal notationsSome0.60section
Ordinal analysisrelated to Ordinal notationsZ20.60section
Ordinal analysisrelated to Ordinal notationsFor0.60section
Ordinal analysisrelated to Ordinal notationsHowever0.60section

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