Ordinal numbers | Proof theory

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. (Wikipedia).

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Related pages

Equiconsistency | Grand conjecture | Primitive recursive arithmetic | Solomon Feferman | Automorphism | Axiom of infinity | Elementary function arithmetic | Jensen hierarchy | Reverse mathematics | Bachmann–Howard ordinal | Feferman–Schütte ordinal | Transfinite induction | Computable function | Peano axioms | Ordinal number | Robinson arithmetic | Zermelo–Fraenkel set theory | Proof theory | Well-order | Grzegorczyk hierarchy | Admissible ordinal | Order type | Second-order arithmetic | First uncountable ordinal | Takeuti–Feferman–Buchholz ordinal | Kleene's O | Kripke–Platek set theory | Intuitionistic logic | Ordinal notation | Well-founded relation | Gentzen's consistency proof | Buchholz psi functions | Complexity class