Skip to main content
Log in

Definable sets and expansions of models of Peano arithmetic

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

We consider expansions of models of Peano arithmetic to models ofA s2 Δ 11 +Σ 11 AC which consist of families of sets definable by nonstandard formulas.

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. Apt, K.R., Marek, W.: Second order arithmetic and related topics. Ann. Math. Logic6, 177–239 (1974)

    Google Scholar 

  2. Barwise, J., Schlipf, J.: On recursively saturated models of arithmetic. In: Saracino, D.H., Weispfenning, V.B. (eds.) Model theory and algebra. (Lect. Notes Math., Vol. 498, pp. 42–55) Berlin Heidelberg New York: Springer 1975

    Google Scholar 

  3. Kaufmann, M.: Mutually generic classes and incompatible expansions. Fund. Math.121, 213–218 (1984)

    Google Scholar 

  4. Kirby, L.: Initial segments of models of arithmetic. Ph. D. Thesis, Manchester University, Manchester 1977

    Google Scholar 

  5. Kirby, L., McAloon, K., Murawski, R.: Indicators, recursive saturation and expandability. Fund. Math.114, 127–139 (1981)

    Google Scholar 

  6. Kirby, L., Paris, J.: Initial segments of models of Peano's axioms. In: Lachlan, A., Srebrny, M., Zarach, A. (eds.) Set theory and hierarchy theory. (Lect. Notes Math., Vol. 619, pp. 211–226) Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  7. Kotlarski, H.: On elementary cuts in recursively saturated models of Peano arithmetic. Fund. Math.120, 205–222 (1984)

    Google Scholar 

  8. Krajewski, S.: Nonstandard satisfaction classes. In: Marek, W., Srebrny, M., Zarach, A. (eds.) Set theory and hierarchy theory. (Lect. Notes Math., Vol. 537, pp. 121–144) Berlin Heidelberg New York: Springer 1976

    Google Scholar 

  9. Mostowski, A.: A remark on models of the Gödel-Bernays axioms for set theory. In: Müller, G.H. (ed.) Sets and classes, pp. 325–340. Amsterdam: North-Holland 1976

    Google Scholar 

  10. Murawski, R.: On expandability of models of Peano arithmetic. I–III. Studia Logica35, 409–419 (1976);35, 421–431 (1976);36, 181–188 (1977)

    Google Scholar 

  11. Murawski, R.: Models of Peano arithmetic expandable to models of fragments of second order arithmetic. Ph. D. Thesis, Warsaw University, Warsaw 1978 (in Polish)

    Google Scholar 

  12. Murawski, R.: Some remarks on the structure of expansions. Z. Math. Logik Grundl. Math.26, 537–546 (1980)

    Google Scholar 

  13. Murawski, R.: Trace expansions of initial segments. Z. Math. Logik Grundl. Math.30, 471–476 (1984)

    Google Scholar 

  14. Murawski, R.: A contribution to nonstandard teratology. In: Müller, G.H., Richter, M.M. (eds.) Models and sets. (Lect. Notes Math., Vol. 1103, pp. 379–388) Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  15. Murawski, R.: Pointwise definable substructures of models of Peano arithmetic. Notre Dame J. Formal Logic (in press)

  16. Schlipf, J.: Toward model theory through recursive saturation. J. Symb. Logic43, 183–206 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Murawski, R. Definable sets and expansions of models of Peano arithmetic. Arch Math Logic 27, 21–33 (1988). https://doi.org/10.1007/BF01625830

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01625830

Keywords

Navigation