Wellordering proofs for metapredicative mahlo

Journal of Symbolic Logic 67 (1):260-278 (2002)
In this article we provide wellordering proofs for metapredicative systems of explicit mathematics and admissible set theory featuring suitable axioms about the Mahloness of the underlying universe of discourse. In particular, it is shown that in the corresponding theories EMA of explicit mathematics and KPm 0 of admissible set theory, transfinite induction along initial segments of the ordinal φω00, for φ being a ternary Veblen function, is derivable. This reveals that the upper bounds given for these two systems in the paper Jager and Strahm [11] are indeed sharp
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DOI 10.2178/jsl/1190150043
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Michael Rathjen (1991). Proof-Theoretic Analysis of KPM. Archive for Mathematical Logic 30 (5-6):377-403.

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