Switch to: Citations

Add references

You must login to add references.
  1. On the Proof-Theoretic Strength of Monotone Induction in Explicit Mathematics.Thomas Glaß, Michael Rathjen & Andreas Schlüter - 1997 - Annals of Pure and Applied Logic 85 (1):1-46.
    We characterize the proof-theoretic strength of systems of explicit mathematics with a general principle asserting the existence of least fixed points for monotone inductive definitions, in terms of certain systems of analysis and set theory. In the case of analysis, these are systems which contain the Σ12-axiom of choice and Π12-comprehension for formulas without set parameters. In the case of set theory, these are systems containing the Kripke-Platek axioms for a recursively inaccessible universe together with the existence of a stable (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  • Monotone Inductive Definitions in a Constructive Theory of Functions and Classes.Shuzo Takahashi - 1989 - Annals of Pure and Applied Logic 42 (3):255-297.
    In this thesis, we study the least fixed point principle in a constructive setting. A constructive theory of functions and sets has been developed by Feferman. This theory deals both with sets and with functions over sets as independent notions. In the language of Feferman's theory, we are able to formulate the least fixed point principle for monotone inductive definitions as: every operation on classes to classes which satisfies the monotonicity condition has a least fixed point. This is called the (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  • Elementary Induction on Abstract Structures.Yiannis N. Moschovakis - 1979 - Journal of Symbolic Logic 44 (1):124-125.
    Direct download  
     
    Export citation  
     
    Bookmark   62 citations  
  • Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
    Direct download  
     
    Export citation  
     
    Bookmark   478 citations  
  • Mathematical Logic.Joseph R. Shoenfield - 1975 - Journal of Symbolic Logic 40 (2):234-236.
    Direct download  
     
    Export citation  
     
    Bookmark   90 citations