Ordinal collapsing function: Difference between revisions

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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 system]]s, typically<ref name="Rathjen-survey">Rathjen, 1995 (Bull. Symbolic Logic)</ref><ref name="Kahle">Kahle, 2002 (Synthese)</ref> subsystems of [[second-order arithmetic|analysis]] (such as those seen in the light of [[reverse mathematics]]), extensions of [[Kripke–Platek set theory]], [[Errett Bishop|Bishop]]-style systems of [[Constructivism (mathematics)|constructive mathematics]] or [[Per Martin-Löf|Martin-Löf]]-style systems of [[intuitionistic type theory]].

([[Psi (letter)|psi]])(1)

Ordinal collapsing functions are typically denoted using some variation of either the Greek letter <math>\psi</math> ([[Psi (letter)|psi]]) or <math>\theta</math> ([[theta]]).