On the proof theory of type two functionals based on primitive recursive operations

✍ Scribed by David Steiner; Thomas Strahm

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 209 KB
• Volume: 52
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200510029

✦ Synopsis

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 E~1~ 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 E~1~ is measured in terms of the two subsystems of second order arithmetic, Π^1^~0~‐CA and Π^1^~1~‐CA, respectively. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)