Skip to main content
SpringerLink
Log in

Countable or ω1-like models of Presburger's arithmetic

  • Conference paper
  • First Online:
Classification Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1292))

  • 384 Accesses

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Friedman, H., "Countable Models of Set Theories," Cambridge Summer School in Mathematical Logic, Springer-Verlag, Lecture Notes in Mathematics #337, 1971, pp. 539–573.

    Google Scholar 

  2. Friedman, H., "Some Systems of Second Order Arithmetic and Their Use," Proceedings of the International Congress of Mathematicians (Vancouver, 1974), Vol. 1, pp. 235–242.

    Google Scholar 

  3. Harnik, V., "ω1-like Recursively Saturated Models of Presburger's Arithmetic," The Journal of Symbolic Logic(1986),Vol. 51,pp. 421–429

    MathSciNet  MATH  Google Scholar 

  4. Lipshitz, L., and Nadel, M., "The Additive Structure of Models of Arithmetic," Proceedings the the AMS 68 (1978), pp. 331–336.

    Article  MathSciNet  MATH  Google Scholar 

  5. MacDowell, R., and Specker, E., "Modelle der Arithmetik," Infinitistic Methods, Pergamon Press, London, 1961, pp. 257–263.

    Google Scholar 

  6. Nadel, M., "On a Problem of MacDowell and Specker," The Journal of Symbolic Logic 45 (1980), pp. 612–622.

    Article  MathSciNet  MATH  Google Scholar 

  7. Nadel, M., and Stavi, J., "On Models of the Elementary Theory of (Z, +, 1)"

    Google Scholar 

  8. Presburger, M., "Über die Vollstandigkeit eines gewissen System der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt," Comptes-rendu du I Congrès des Mathématiciens des Pays Slaves, Wassaw, 1930, pp. 92–101, 395.

    Google Scholar 

  9. D. Scott, "Algebras of Sets Binumerable in Complete Extensions of Arithmetic," Recursive Function Theory, Proc. Sympos. Pure Math., Vol. 5, AMS, 1962, pp. 117–121.

    Article  MathSciNet  MATH  Google Scholar 

  10. Smorynski, C., "Lectures on Nonstandard Models of Arithmetic," Logic Colloquium 82, ed. G. Lolli, G. Longo and A. Marcja, North-Holland, Amsterdam, 1984, pp. 1–70.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Haifa, Haifa, Israel

    Victor Harnik

Authors
  1. Victor Harnik
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

John T. Baldwin

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Harnik, V. (1987). Countable or ω1-like models of Presburger's arithmetic. In: Baldwin, J.T. (eds) Classification Theory. Lecture Notes in Mathematics, vol 1292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082233

Download citation

  • DOI: https://doi.org/10.1007/BFb0082233

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18674-8

  • Online ISBN: 978-3-540-48049-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation