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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 than the one being defined, perhaps even large cardinals (though they can be replaced with recursively large ordinals at the cost of extra technical difficulty), and then "collapse" them down to a system of notations for the sought-after ordinal. For this reason, ordinal collapsing functions are described as an impredicative manner of naming ordinals.

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rdfs:label	Fonction d'effondrement ordinale (fr) Ordinal collapsing function (en)
rdfs:comment	En logique mathématique et en théorie des ensembles, une fonction d'effondrement ordinale (en anglais, ordinal collapsing function) est une méthode de définition de notations pour certains grands ordinaux dénombrables, consistant à donner des noms à certains ordinaux beaucoup plus grands que ceux que l'on veut noter, puis à les « effondrer » pour obtenir le système de notations cherché. (fr) 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 than the one being defined, perhaps even large cardinals (though they can be replaced with recursively large ordinals at the cost of extra technical difficulty), and then "collapse" them down to a system of notations for the sought-after ordinal. For this reason, ordinal collapsing functions are described as an impredicative manner of naming ordinals. (en)
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Link from a Wikipage to another Wikipage	Monotonic function Peano arithmetic Peano axioms Per Martin-Löf Reverse mathematics Indescribable cardinal Intuitionistic type theory Continuous function Mathematical logic Noriko H. Arai Church–Kleene ordinal Epsilon numbers (mathematics) Theta Ordinal analysis Ordinal arithmetic Ordinal notation Feferman–Schütte ordinal Kripke–Platek set theory Kruskal's tree theorem Mahlo cardinal Well-founded relation Large Veblen ordinal Large countable ordinal Errett Bishop Bar induction Nonrecursive ordinal Formal system Goodstein's theorem Reflection principle Bachmann–Howard ordinal Ackermann function Ackermann ordinal Ordinal numbers Cofinality Weakly compact cardinal Constructivism (philosophy of mathematics) Impredicativity Inaccessible cardinal Buchholz's ordinal Cantor's diagonal argument Recursive ordinal Set theory Small Veblen ordinal Second-order arithmetic Existential quantification First uncountable ordinal Psi (letter) Veblen function Cantor normal form theorem Takeuti–Feferman–Buchholz ordinal Large cardinal property Countable ordinal
Link from a Wikipage to an external page	http://www.mathematik.uni-muenchen.de/~aehlig/EST/rathjen4.pdf https://web.archive.org/web/20070612112202/http:/www.mathematik.uni-muenchen.de/~aehlig/EST/rathjen4.pdf https://epub.ub.uni-muenchen.de/3841/ https://www.math.ucla.edu/~asl/bsl/0104/0104-004.ps http://www.maths.leeds.ac.uk/~rathjen/NSTAB.ps http://www.maths.leeds.ac.uk/~rathjen/ehab.pdf
sameAs	Ordinal collapsing function Ordinal collapsing function Ordinal collapsing function Ordinal collapsing function Ordinal collapsing function
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has abstract	En logique mathématique et en théorie des ensembles, une fonction d'effondrement ordinale (en anglais, ordinal collapsing function) est une méthode de définition de notations pour certains grands ordinaux dénombrables, consistant à donner des noms à certains ordinaux beaucoup plus grands que ceux que l'on veut noter, puis à les « effondrer » pour obtenir le système de notations cherché. (fr) 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 than the one being defined, perhaps even large cardinals (though they can be replaced with recursively large ordinals at the cost of extra technical difficulty), and then "collapse" them down to a system of notations for the sought-after ordinal. For this reason, ordinal collapsing functions are described as an impredicative manner of naming ordinals. The details of the definition of ordinal collapsing functions vary, and get more complicated as greater ordinals are being defined, but the typical idea is that whenever the notation system "runs out of fuel" and cannot name a certain ordinal, a much larger ordinal is brought "from above" to give a name to that critical point. An example of how this works will be detailed below, for an ordinal collapsing function defining the Bachmann–Howard ordinal (i.e., defining a system of notations up to the Bachmann–Howard ordinal). The use and definition of ordinal collapsing functions is inextricably intertwined with the theory of ordinal analysis, since the large countable ordinals defined and denoted by a given collapse are used to describe the ordinal-theoretic strength of certain formal systems, typically subsystems of analysis (such as those seen in the light of reverse mathematics), extensions of Kripke–Platek set theory, Bishop-style systems of constructive mathematics or Martin-Löf-style systems of intuitionistic type theory.(psi)(1) Ordinal collapsing functions are typically denoted using some variation of either the Greek letter (psi) or (theta). (en)
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is Link from a Wikipage to another Wikipage of	List of forcing notions Kurepa tree OCF Theta Arai psi function Arai ψ function Feferman–Schütte ordinal Psi (Greek) Heinz Bachmann Large countable ordinal Nonrecursive ordinal Psi function

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