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¶
Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.
Does it back the claim? Not recorded. The single citation of this work carries no recorded support check.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
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Registry ID ref:e0a5774a4304 · see in the full table