Switch to: Citations

References in:

Relative arithmetic

Mathematical Logic Quarterly 56 (6):564-572 (2010)

Add references

You must login to add references.
  1. More infinity for a better finitism.Sam Sanders - 2010 - Annals of Pure and Applied Logic 161 (12):1525-1540.
    Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis with a PRA consistency proof, proposed in around 1995 by Patrick Suppes and Richard Sommer. It is based on an earlier system developed by Rolando Chuaqui and Patrick Suppes. Here, we discuss the inherent problems and limitations of the classical nonstandard framework and propose a much-needed refinement of ERNA, called , in the spirit of Karel Hrbacek’s stratified set theory. We study the metamathematics of and its (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Internal Set Theory: A New Approach to Nonstandard Analysis.Edward Nelson - 1977 - Journal of Symbolic Logic 48 (4):1203-1204.
    Direct download  
     
    Export citation  
     
    Bookmark   60 citations  
  • Nonstandard arithmetic and reverse mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
    We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [3] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles which are equivalent in strength to weaker theories in second order arithmetic.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   18 citations  
  • Transfer and a Supremum Principle for ERNA.Chris Impens & Sam Sanders - 2008 - Journal of Symbolic Logic 73 (2):689 - 710.
    Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis proposed around 1995 by Patrick Suppes and Richard Sommer, who also proved its consistency inside PRA. It is based on an earlier system developed by Rolando Chuaqui and Patrick Suppes, of which Michal Rössler and Emil Jeřábek have recently proposed a weakened version. We add a Π₁-transfer principle to ERNA and prove the consistency of the extended theory inside PRA. In this extension of ERNA a σ₁-supremum (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations