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Axiomatization of the monadic second order theory of ω1

Part of the Lecture Notes in Mathematics book series (LNM,volume 328)

Keywords

  • Axiom System
  • Order Theory
  • Propositional Formula
  • True Sentence
  • Pigeon Hole Principle

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References

  1. Garrett Birkhoff, "Lattice Theory". AMS Coll. Publ. 25, Providence 1963

    Google Scholar 

  2. J. Richard Büchi, "Weak second order arithmetic and finite automata". Z. Math. Logik Grundl. Math. 6 (1960), 66–92

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. J. Richard Büchi, "On a decision method in restricted second order arithmetic". In "Logic Meth. Phil. Sc., Proc. 1960 Stanford Intern. Congr.", Stanford 1962, 1–11

    Google Scholar 

  4. J Richard Büchi, "Transfinite automata recursions and weak second order theory of ordinals". In "Logic Meth. Phil. Sc., Proc. 1964 Jerusalem Intern. Congr.", Amsterdam 1965, 3–23

    Google Scholar 

  5. J. Richard Büchi, "Decision methods in the theory of ordinals". Bull. AMS 71 (1965), 767–770

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. J. Richard Büchi, "The monadic second order theory of ω1". This volume.

    Google Scholar 

  7. J. Richard Büchi, Dirk Siefkes, "The complete extensions of the monadic second order theory of countable ordinals". To appear

    Google Scholar 

  8. Alonzo Church, "Alternatives to Zermelo's assumption". Trans. AMS 29 (1927), 178–208

    MathSciNet  MATH  Google Scholar 

  9. Alonzo Church, "Introduction to mathematical logic. I". Princeton 1956

    Google Scholar 

  10. Peter Hájek, "The consistency of Church's alternatives". Bull. Acad. Pol. Sc. 14 (1966), 423–430

    MATH  Google Scholar 

  11. Leo Henkin, "Completeness in the theory of types". J. Symb. Logic 15 (1950), 81–91

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Leo Henkin, "Banishing the rule of substitution for functional variables". J. Symb. Logic 18 (1953), 201–208

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Thomas J. Jech, "ω1 can be measurable". Israel J. Math. 6 (1968), 363–367

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Azriel Levi, "I present here an outline …". Unpublished manuscript

    Google Scholar 

  15. Ami Litman, "On the decidability of the monadic theory of ω1". M. Sc. thesis, The Hebrew University, Jerusalem 1972 (Hebrew)

    Google Scholar 

  16. Andrzej Mostowski, Alfred Tarski, "Arithmetical classes and types of well-ordered systems". Bull. AMS 55 (1949), 65 (abstract)

    Google Scholar 

  17. Andrzej Mostowski, Alfred Tarski, "The elementary theory of well ordering". Unpublished.

    Google Scholar 

  18. Jan Mycielski, "On the axiom of determinateness". Fund. Math. 53 (1963/64), 205–224

    MathSciNet  MATH  Google Scholar 

  19. Saharon Shelah, "The monadic theory of order". Institute of Mathematics, The Hebrew University, Jerusalem, Israel, Winter 1972/73

    MATH  Google Scholar 

  20. Dirk Siefkes, "Decidable Theories I. Büchi's monadic second order successor arithmetic". Lect. Notes Math. 120, Berlin Heidelberg New York 1970

    Google Scholar 

  21. Dirk Siefkes, "Recursive models for certain monadic second order fragments of arithmetic". To appear

    Google Scholar 

  22. Thoralf Skolem, "Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre". Proc. 5th Scand. Math. Congr. Helsinki 1922, 217–232

    Google Scholar 

  23. Thoralf Skolem, "Über einige Grundlagenfragen der Mathematik". Skrifter Vitenskapsakademiet i Oslo I, No. 4 (1929), 1–49

    Google Scholar 

  24. Thoralf Skolem, "Über die Nichtcharakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Aussagen mit ausschließlich Zahlenvariablen". Fund. Math. 23 (1934), 150–161

    MATH  Google Scholar 

  25. Ernst Specker, "Zur Axiomatik der Mengenlehre (Fundierungs-und Auswahlaxiom)". Z. Math. Logik Grundl. Math. 3 (1957), 173–210

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1973 Springer-Verlag

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Büchi, J.R., Siefkes, D. (1973). Axiomatization of the monadic second order theory of ω1 . In: Müller, G.H., Siefkes, D. (eds) Decidable Theories II. Lecture Notes in Mathematics, vol 328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082722

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  • DOI: https://doi.org/10.1007/BFb0082722

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  • Print ISBN: 978-3-540-06345-2

  • Online ISBN: 978-3-540-46946-9

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