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Countable or ω1-like models of Presburger's arithmetic

  • Victor Harnik
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1292)

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References

  1. [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. [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. [3]
    Harnik, V., "ω1-like Recursively Saturated Models of Presburger's Arithmetic," The Journal of Symbolic Logic(1986),Vol. 51,pp. 421–429MathSciNetzbMATHGoogle Scholar
  4. [4]
    Lipshitz, L., and Nadel, M., "The Additive Structure of Models of Arithmetic," Proceedings the the AMS 68 (1978), pp. 331–336.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    MacDowell, R., and Specker, E., "Modelle der Arithmetik," Infinitistic Methods, Pergamon Press, London, 1961, pp. 257–263.Google Scholar
  6. [6]
    Nadel, M., "On a Problem of MacDowell and Specker," The Journal of Symbolic Logic 45 (1980), pp. 612–622.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Nadel, M., and Stavi, J., "On Models of the Elementary Theory of (Z, +, 1)"Google Scholar
  8. [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. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [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.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Victor Harnik
    • 1
  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael

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