The art of ordinal analysis.¶
Rathjen, M. (2006). The art of ordinal analysis. Proceedings of the International Congress of Mathematicians 2006, Madrid.
Cited by¶
1 citation across 1 artifact.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Well-Foundedness (Well-Ordering)
- … by the ordinals needed to prove their consistency (PA at ε₀; systems of second-order arithmetic at larger ordinals — ATR₀ at Γ₀, predicative analysis at the Feferman-Schütte ordinal, Π¹₁-comprehension at the Bachmann-Howard ordinal; ZFC's proof-theoretic ordinal is unknown and the subject of ongoing research).
This sourceSurvey of proof-theoretic ordinals across PA, ATR₀, predicative analysis, and impredicative theories.
- … by the ordinals needed to prove their consistency (PA at ε₀; systems of second-order arithmetic at larger ordinals — ATR₀ at Γ₀, predicative analysis at the Feferman-Schütte ordinal, Π¹₁-comprehension at the Bachmann-Howard ordinal; ZFC's proof-theoretic ordinal is unknown and the subject of ongoing research).
Verification¶
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Registry ID ref:e0a5774a4304 · see in the full table