Ramsey quantifiers in arithmetic

  • Angus Macintyre
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 834)


Completeness Theorem Springer Lecture Note Peano Arithmetic Inductive Structure Nonstandard Model 
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  1. [BMK]
    J. Barwise, M. Makkai, M. Kaufmann, Stationary logic, Ann. Math. Logic 13, 171–224.Google Scholar
  2. [EM]
    A. Ehrenfeucht and A. Mostowski, Models of axiomatic theories admitting automorphisms, Fund. Math. 43, 50–68.Google Scholar
  3. [ER]
    P. Erdos and R. Rado, A partition calculus in set theory, B.A.M.S. 62 (1956), 427–489.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [F1]
    H. Friedman, Countable models of set theories, 539–573 in Proceedings of Cambridge Summer School in Mathematical Logic (ed. Mathias) Springer Lecture Notes 337, 1973.Google Scholar
  5. [F2]
    _____, Systems of second order arithmetic with restricted induction I, II, J.S.L. 41 (1976), 557–557.Google Scholar
  6. [F3]
    _____, preprints on Borel Diagonalization, Ohio State, 1979.Google Scholar
  7. [F4]
    _____, Borel structures in mathematics, preprint, Ohio State, 1979.Google Scholar
  8. [FMS]
    H. Friedman, K. McAloon, S. Simpson, A finite combinatorial principle which is equivalent to the 1-consistency of predicative analysis, in preparation.Google Scholar
  9. [G1]
    H. Gaifman, Models and types of Peano arithmetic, Annals Math. Logic 9 (1976), 223–306.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [G2]
    _____, A note on models and submodels of arithmetic, 128–144, in Conference in Mathematical Logic London 1970 (ed. W. Hodges), Springer Lecture Notes 255, 1972.Google Scholar
  11. [Go]
    K. Godel, Uber formal unentscheidbare Satze der Principia Mathematica and verwandter Systeme, 1, Monatsh. Math. Phys. 38 (1931), 173–198.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [J]
    C. Jockusch, Ramsey’s theorem and recursion theory, J.S.L. 37 (1972), 268–280.MathSciNetzbMATHGoogle Scholar
  13. [KP]
    L. Kirby and J. Paris, Initial segments of models of Peano’s axioms, 211–246 in Set Theory and Hierarchy Theory V (ed. A. H. Lachlan, M. Srebrny, Springer Lecture Notes 619, 1977.Google Scholar
  14. [K]
    S. Krajewski, Nonstandard satisfaction classes, 121–144 in Set Theory and Hierarchy Theory in memory of A. Mostowski (ed. W. Marek), Springer Lecture Notes 537, 1976.Google Scholar
  15. [L]
    P. Lindstrom, On extensions of elementary logic, Theoria 35 (1969), 1–11.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [MM]
    M. Magidor and J. Malitz, Compact extensions of L(Q), 1(a), Annals Math. Logic 11 (1977), 217–261.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [Ma]
    A. Macintyre, Generalized quantifiers in arithmetic, Abstract 755-E11, Notices of A.M.S. 25 (1978), A–386.Google Scholar
  18. [MS]
    A. Macintyre and H. Simmons, Algebraic properties of number theories, Israel Journal 22 (1975), 7–27.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [Mc 1]
    K. McAloon, Formes combinatoires du Theoreme d’Incomplé-tude, 263–277 in Seminaire Bourbaki 1977/78, Springer Lecture Notes 710, 1979.Google Scholar
  20. [Mc 2]
    _____, Completeness theorems, incompleteness theorems and models of arithmetic, T.A.M.S. 239, 253–277.Google Scholar
  21. [Mo]
    C. Morgenstern, On generalized quantifiers in arithmetic, to appear in J.S.L.Google Scholar
  22. [PH]
    J. Paris and L. Harrington, A mathematical incompleteness in Peano arithmetic, 1133–1142 in Handbook of Mathematical Logic (ed. J. Barwise), North Holland, 1977.Google Scholar
  23. [Ra]
    M. Rabin, Diophantine equations and nonstandard models of arithmetic, 151–158 in Proceedings of 1960 I.C.L.M.S., (ed. Nagell Stanford, 1960.Google Scholar
  24. [S]
    J. Schlipf, Scribblings on papers of Kirby and Paris and Paris and Harrington, Abstract 755-E16, Notices A.M.S. 25 (1978), A–387.Google Scholar
  25. [Sch]
    J. Schmerl, Extending models of arithmetic, Annals. Math. Logic 14 (1978), 89–109.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [SS]
    J. Schmerl and S. Simpson, On the role of Ramsey quantifiers in first-order arithmetic, to appear in J.S.L.Google Scholar
  27. [She 1]
    S. Shelah, unpublished.Google Scholar
  28. [She 2]
    _____, Omitting Types Theorem for L(Q), notes by W. Hodges, Bedford College, London, 1978.Google Scholar
  29. [Sho]
    J. Shoenfield, Mathematical Logic, Addison-Wesley 1967.Google Scholar
  30. [So]
    R. Solovay, A model of set theory in which every set of reals is Lebesgue measurable, Annals Math. 92 (1970), 1–56.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [SK]
    R. Solovay and J. Ketonen, Rapidly growing Ramsey functions, to appear.Google Scholar
  32. [T]
    S. Tennenbaum, unpublished.Google Scholar
  33. [W]
    A. Wilkie, On the theories of end-extensions of models of arithmetic, 305–310 in Set Theory and Hierarchy Theory V (ed. A. H. Lachlan, M. Srebrny, A. Zarach), Springer Lecture Notes 619, 1977.Google Scholar

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© Springer-Verlag 1980

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  • Angus Macintyre

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