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constructive ordinal

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  • 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 logic — In mathematics, ordinal logic is a logic associated with an ordinal number by recursively adding elements to a sequence of previous logics.[1][2] The concept was introduced in 1938 by Alan Turing in his PhD dissertation at Princeton in view of… …   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 — Nombre ordinal En linguistique, les mots premier, deuxième, troisième, quatrième, etc. s appellent des adjectifs numéraux ordinaux qui servent à préciser le rang d un objet dans une collection ou l ordre d un événement dans une succession. Cette… …   Wikipédia en Français

  • 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

  • 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

  • Bachmann–Howard ordinal — In mathematics, the Bachmann–Howard ordinal (or Howard ordinal) is a large countable ordinal.It is the proof theoretic ordinal of several mathematical theories, such as Kripke–Platek set theory (with the axiom of infinity) and the system CZF of… …   Wikipedia

  • Nombre Ordinal — En linguistique, les mots premier, deuxième, troisième, quatrième, etc. s appellent des adjectifs numéraux ordinaux qui servent à préciser le rang d un objet dans une collection ou l ordre d un événement dans une succession. Cette notion se… …   Wikipédia en Français

  • Nombre ordinal — En mathématiques, on appelle nombre ordinal un objet permettant de caractériser le type d ordre d un ensemble bien ordonné quelconque. Comme, en linguistique, les mots premier, deuxième, troisième, quatrième, etc. s appellent des adjectifs… …   Wikipédia en Français

  • 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

  • Gentzen's consistency proof — Gentzen s theoremIn 1936 Gerhard Gentzen proved the consistency of first order arithmetic using combinatorial methods. Gentzen s proof shows much more than merely that first order arithmetic is consistent. Gentzen showed that the consistency of… …   Wikipedia

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