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The Recursively Mahlo Property in Second Order Arithmetic
Mathematical Logic Quarterly 42 (1):59-66 (1996)
Abstract
The paper characterizes the second order arithmetic theorems of a set theory that features a recursively Mahlo universe; thereby complementing prior proof-theoretic investigations on this notion. It is shown that the property of being recursively Mahlo corresponds to a certain kind of β-model reflection in second order arithmetic. Further, this leads to a characterization of the reals recursively computable in the superjump functionalAuthor's Profile
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Citations of this work
On the mathematical and foundational significance of the uncountable.Dag Normann & Sam Sanders - 2019 - Journal of Mathematical Logic 19 (1):1950001.
The Constructive Hilbert Program and the Limits of Martin-Löf Type Theory.Michael Rathjen - 2005 - Synthese 147 (1):81-120.
A Sneak Preview of Proof Theory of Ordinals.Toshiyasu Arai - 2012 - Annals of the Japan Association for Philosophy of Science 20:29-47.
References found in this work
Admissible sets and structures: an approach to definability theory.Jon Barwise - 1975 - New York: Springer Verlag.
Set Theory: An Introduction to Large Cardinals.F. R. Drake & T. J. Jech - 1976 - British Journal for the Philosophy of Science 27 (2):187-191.
Set Theory. An Introduction to Large Cardinals.Azriel Levy - 1978 - Journal of Symbolic Logic 43 (2):384-384.
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