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
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| 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
Systems of Explicit Mathematics with Non-Constructive Μ-Operator. Part I.Solomon Feferman & Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 65 (3):243-263.
Totality in Applicative Theories.Gerhard Jäger & Thomas Strahm - 1995 - Annals of Pure and Applied Logic 74 (2):105-120.
Some Theories with Positive Induction of Ordinal Strength Φω.Gerhard Jäger & Thomas Strahm - 1996 - Journal of Symbolic Logic 61 (3):818-842.
Systems of Explicit Mathematics with Non-Constructive Μ-Operator and Join.Thomas Glaß & Thomas Strahm - 1996 - Annals of Pure and Applied Logic 82 (2):193-219.
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