About: Rathjen's psi function

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In mathematics, Rathjen's psi function is an ordinal collapsing function developed by Michael Rathjen. It collapses weakly Mahlo cardinals to generate large countable ordinals. A weakly Mahlo cardinal is a cardinal such that the set of regular cardinals below is closed under (i.e. all normal functions closed in are closed under some regular ordinal ). Rathjen uses this to diagonalise over the weakly inaccessible hierarchy.

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  • In mathematics, Rathjen's psi function is an ordinal collapsing function developed by Michael Rathjen. It collapses weakly Mahlo cardinals to generate large countable ordinals. A weakly Mahlo cardinal is a cardinal such that the set of regular cardinals below is closed under (i.e. all normal functions closed in are closed under some regular ordinal ). Rathjen uses this to diagonalise over the weakly inaccessible hierarchy. It admits an associated ordinal notation whose limit (i.e. ordinal type) is , which is strictly greater than both and the limit of countable ordinals expressed by Rathjen's . , which is called the "Small Rathjen ordinal" is the proof-theoretic ordinal of , Kripke–Platek set theory augmented by the axiom schema "for any -formula satisfying , there exists an addmissible set satisfying ". It is equal to in Rathjen's function. (en)
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  • In mathematics, Rathjen's psi function is an ordinal collapsing function developed by Michael Rathjen. It collapses weakly Mahlo cardinals to generate large countable ordinals. A weakly Mahlo cardinal is a cardinal such that the set of regular cardinals below is closed under (i.e. all normal functions closed in are closed under some regular ordinal ). Rathjen uses this to diagonalise over the weakly inaccessible hierarchy. (en)
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  • Rathjen's psi function (en)
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