Skip to main content
Log in

Subsets coded in elementary end extensions

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

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.

References

  1. Avigad J.: Formalizing forcing arguments in subsystems of second-order arithmetic. Ann. Pure Appl. Logic 82, 165–191 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cholak P.A., Jockusch C.G. Jr, Slaman T.A.: On the strength of Ramsey’s theorem for pairs. J. Symb. Log. 66, 1–55 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cholak P.A., Jockusch C.G. Jr, Slaman T.A.: Corrigendum to: “On the strength of Ramsey’s theorem for pairs”. J. Symb. Log. 74, 1438–1439 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  4. Gaifman, H.: On local arithmetical functions and their application for constructing types of Peano’s arithmetic. In: Mathematical Logic and Foundations of Set Theory (Proceedings of International Colloquium, Jerusalem, 1968) North-Holland, Amsterdam, pp. 105–121 (1970)

  5. Hájek, P.: Interpretability and fragments of arithmetic. In: Clote, P., Krajíček, J. (eds.) Arithmetic, Proof Theory, and Computational Complexity (Prague, 1991), Oxford Logic Guides, vol. 23. Oxford University Press, New York, 1993, pp. 185–196

  6. Kanovei, V.: On “star” schemata of Kossak and Paris. In: Logic Colloquium ‘96 (San Sebastián), Lecture Notes in Logic, vol. 12, Springer, Berlin, pp. 101–114 (1998)

  7. Kossak R.: A note on a theorem of Kanovei. Arch. Math. Log. 43, 565–569 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kossak, R., Paris, J.B.: Subsets of models of arithmetic, In: Guzicki, W., et al. (eds.) Open Days in Model Theory and Set Theory: Proceedings of a Conference Held in September 1981 at Jadwisin, Near Warsaw, Poland, Leeds, pp. 159–174 (1983)

  9. Kossak R., Paris J.B.: Subsets of models of arithmetic. Arch. Math. Log. 32, 65–73 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kossak R., Schmerl J.H.: The Structure of Models of Peano Arithmetic. Oxford University Press, Oxford (2006)

    Book  MATH  Google Scholar 

  11. MacDowell, R., Specker, E.: Modelle der Arithmetik. In: Infinitistic Methods (Proceedings Symposium on Foundations of Mathematics, Warsaw, 1959) Pergamon, Oxford, Warsaw, pp. 257–263 (1961)

  12. Phillips, R.G.: Omitting types in arithmetic and conservative extensions. In: Victoria Symposium on Nonstandard Analysis (University of Victoria, Victoria, B.C., 1972), Lecture Notes in Mathematics, vol. 369. Springer, Berlin, pp. 195–202 (1974)

  13. Simpson S.G.: Subsystems of Second Order Arithmetic, Perspectives in Logic, 2nd edn. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  14. Towsner, H.: On maximal conservative extensions, arXiv:1302.1488v2 (2013)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to James H. Schmerl.

Additional information

Thanks to Roman Kossak and Athar Abdul-Quader whose constructive comments lead to, among other things, a simplification in the proof of Theorem 4.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schmerl, J.H. Subsets coded in elementary end extensions. Arch. Math. Logic 53, 571–581 (2014). https://doi.org/10.1007/s00153-014-0381-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-014-0381-z

Keywords

Mathematics Subject Classification

Navigation