Skip to main content
Log in

Models of Arithmetic and recursive functions

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We investigate homomorphic images of the semiring of recursive functions as models of the Π2 fragment of Arithmetic, and some relations between this fragment, its models and recursion theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Feferman, D. Scott and S. Tennenbaum.Models of arithmetic through function rings, Notices of the Amer. Math. Soc.173 (1959).

  2. H. Gaifman,A note on models and submodels of arithmetic, Conference in Mathematical Logic, London, 1970, Springer Verlag 1972, pp. 128–144.

  3. J. Hirschfeld,Models of Arithmetic and the semiring of recursive functions, Victoria Symposium on Non-Standard Analysis, Spring Verlag, 1974, pp. 99–105.

  4. H. J. Keisler,Limit ultrapowers, Trans. Amer. Math. Soc.107 (1972), 382–408.

    Article  MathSciNet  Google Scholar 

  5. M. eerman, Doctoral Dissertation, Cornell University, (1968).

  6. M. Lerman,Recursive functions modulo co-r-maximal sets, Trans. Amer. Math. Soc.148 (1970), 429–444.

    Article  MATH  MathSciNet  Google Scholar 

  7. Yu. V. Matijasevic,Diophantine representation of recursively enumerable predicates Proceeding of the second Scandinavian logic symposium, North-Holland (1971).

  8. A. Robinson,Model theory and non-standard arithmetic, Infinitistic methods, Proceeding of the symposium in Warsaw (1959), 265–302.

  9. J. R. Shonfield,Mathematical logic, Addison-Weseley, 1967.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hirschfeld, J. Models of Arithmetic and recursive functions. Israel J. Math. 20, 111–126 (1975). https://doi.org/10.1007/BF02757881

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02757881

Keywords

Navigation