Mathematical Logic Quarterly 52 (3):237-252 (2006)

Abstract
This paper is a companion to work of Feferman, Jäger, Glaß, and Strahm on the proof theory of the type two functionals μ and E1 in the context of Feferman-style applicative theories. In contrast to the previous work, we analyze these two functionals in the context of Schlüter's weakened applicative basis PRON which allows for an interpretation in the primitive recursive indices. The proof-theoretic strength of PRON augmented by μ and E1 is measured in terms of the two subsystems of second order arithmetic, Π10-CA and Π11-CA, respectively
Keywords applicative theories  primitive recursion  Proof theory  type two functionals
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DOI 10.1002/malq.200510029
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References found in this work BETA

Definedness.Solomon Feferman - 1995 - Erkenntnis 43 (3):295 - 320.
Totality in Applicative Theories.Gerhard Jäger & Thomas Strahm - 1995 - Annals of Pure and Applied Logic 74 (2):105-120.
Polytime, Combinatory Logic and Positive Safe Induction.Cantini Andrea - 2002 - Archive for Mathematical Logic 41 (2):169-189.

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