Switch to: References

Add citations

You must login to add citations.
  1. Universes Over Frege Structures.Reinhard Kahle - 2003 - Annals of Pure and Applied Logic 119 (1-3):191-223.
    In this paper, we study a concept of universe for a truth predicate over applicative theories. A proof-theoretic analysis is given by use of transfinitely iterated fixed point theories . The lower bound is obtained by a syntactical interpretation of these theories. Thus, universes over Frege structures represent a syntactically expressive framework of metapredicative theories in the context of applicative theories.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Universes in Explicit Mathematics.Gerhard Jäger, Reinhard Kahle & Thomas Studer - 2001 - Annals of Pure and Applied Logic 109 (3):141-162.
    This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed. Later, we turn to least universes, strictness and name induction. Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent to Feferman's.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  • The Proof-Theoretic Analysis of Transfinitely Iterated Fixed Point Theories.Gerhard JÄger, Reinhard Kahle, Anton Setzer & Thomas Strahm - 1999 - Journal of Symbolic Logic 64 (1):53-67.
    This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{ the exact proof-theoretic ordinals of these systems are presented.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  • The Non-Constructive Μ Operator, Fixed Point Theories with Ordinals, and the Bar Rule.Thomas Strahm - 2000 - Annals of Pure and Applied Logic 104 (1-3):305-324.
    This paper deals with the proof theory of first-order applicative theories with non-constructive μ operator and a form of the bar rule, yielding systems of ordinal strength Γ0 and 20, respectively. Relevant use is made of fixed-point theories with ordinals plus bar rule.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations