Upper Bounds for metapredicative mahlo in explicit mathematics and admissible set theory

Journal of Symbolic Logic 66 (2):935-958 (2001)
In this article we introduce systems for metapredicative Mahlo in explicit mathematics and admissible set theory. The exact upper proof-theoretic bounds of these systems are established
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Reinhard Kahle (2003). Universes Over Frege Structures. Annals of Pure and Applied Logic 119 (1-3):191-223.
Gerhard Jäger (2007). On Feferman's Operational Set Theory. Annals of Pure and Applied Logic 150 (1):19-39.

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