Ordinal de Feferman-Schütte

Ordinal de Feferman-Schütte

En mathématiques, et plus précisément en théorie des ensembles, l’ordinal de Feferman–Schütte, noté Γ0, est un grand ordinal dénombrable, étudié par Solomon Feferman (en) et Kurt Schütte (en).

Définition

L'ordinal de Feferman–Schütte est le plus petit ordinal qui ne peut être atteint à partir de 0 en utilisant seulement l'addition des ordinaux et les fonctions de Veblen (en) φα(β).Autrement dit, c'est le plus petit α tel que φα(0) = α.

Propriétés

Références


  • (en) Wolfram Pohlers, Proof theory, vol. 1407, Berlin, Springer-Verlag, 1989 (ISBN 3-540-51842-8) 
  • (en) Nik Weaver, Predicativity beyond Gamma_0, 2005 

Wikimedia Foundation. 2010.

Contenu soumis à la licence CC-BY-SA. Source : Article Ordinal de Feferman-Schütte de Wikipédia en français (auteurs)

Игры ⚽ Поможем написать реферат

Regardez d'autres dictionnaires:

  • Feferman–Schütte ordinal — In mathematics, the Feferman–Schütte ordinal Gamma;0 is a large countable ordinal.It is the proof theoretic ordinal of several mathematical theories.It is named after Solomon Feferman and Kurt Schütte.It is sometimes said to be the first… …   Wikipedia

  • Ordinal analysis — In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength. The field was formed when Gerhard Gentzen in 1934 used cut elimination to prove, in modern terms, that… …   Wikipedia

  • Ordinal collapsing function — In mathematical logic and set theory, an ordinal collapsing function (or projection function) is a technique for defining (notations for) certain recursive large countable ordinals, whose principle is to give names to certain ordinals much larger …   Wikipedia

  • Ordinal notation — In mathematical logic and set theory, an ordinal notation is a finite sequence of symbols from a finite alphabet which names an ordinal number according to some scheme which gives meaning to the language. There are many such schemes of ordinal… …   Wikipedia

  • Ordinal number — This article is about the mathematical concept. For number words denoting a position in a sequence ( first , second , third , etc.), see Ordinal number (linguistics). Representation of the ordinal numbers up to ωω. Each turn of the spiral… …   Wikipedia

  • Large countable ordinal — In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of… …   Wikipedia

  • Kurt Schütte — 14 October 1909 (Salzwedel) ndash; 18 August 1998 was a German mathematician who worked on proof theory and ordinal analysis. The Feferman Schütte ordinal, which he showed to be the precise ordinal bound for predicativity, is named after… …   Wikipedia

  • Church–Kleene ordinal — In mathematics, the Church–Kleene ordinal, , is a large countable ordinal. It is the smallest non recursive ordinal. It is named after Alonzo Church and S. C. Kleene. References Church, Alonzo; Kleene, S. C. (1937), Formal definitions in the… …   Wikipedia

  • Small Veblen ordinal — In mathematics, the small Veblen ordinal is a certain large countable ordinal, named after Oswald Veblen. It is occasionally called the Ackermann ordinal, though the Ackermann ordinal described by harvtxt|Ackermann|1951 is somewhat smaller than… …   Wikipedia

  • Ackermann ordinal — In mathematics, the Ackermann ordinal is a certain large countable ordinal, named after Wilhelm Ackermann. The term Ackermann ordinal is also occasionally used for the small Veblen ordinal, a somewhat larger ordinal. Unfortunately there is no… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”