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The monadic second order theory of ω1

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

Keywords

  • Linear Order
  • Terminal Condition
  • Inductive Assumption
  • Order Theory
  • Finite Automaton

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Bibliography

  1. J.R. Büchi, Weak second order arithmetic and finite automata, Z. Math. Logik und Grundl. Math. 6 (1960), 66–92.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. _____, On a decision method in restricted second order arithmetic, Proc. 1960 Int. Cong. for Logic, Method and Philos. of Sci., Stanford Univ. Press, Stanford, Calif., 1962.

    MATH  Google Scholar 

  3. _____, Decision methods in the theory of ordinals, Bull. Am. Math. Soc. 71 (1965), 767–770.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. _____, Transfinite automata recursions and weak second order theory of ordinals, Proc. 1964 Int. Cong. for Logic, Method and Philos. of Sci., North-Holland Publishing Co., Amsterdam, 1965.

    MATH  Google Scholar 

  5. Büchi and Landweber, Solving sequential conditions by finite-state strategies, Trans. Am. Math. Soc. 138 (1969), 295–311.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. __________, Definability in the monadic second-order theory of successor, Journ. Sym. Logic 34 (1969), 166–170.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. A. Church, Logic arithmetic and automata, Proc. Int. Congr. Math 1962, Almquist and Wiksells, Uppsala, 1963.

    MATH  Google Scholar 

  8. J. Doner, Tree acceptors and some of their applications, Journ. Computer and System Sci. 4 (1970), 406–451.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. A. Ehrenfeucht, Application of games to the completeness problem for formalized theories, Fund. Math. 49 (1960–61), 129–141.

    MathSciNet  MATH  Google Scholar 

  10. C.C. Elgot, Decision problems of finite automata design and related arithmetics, Trans. Am. Math. Soc. 98 (1961), 21–51.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Feferman and Vaught, The first order properties of products of algebraic systems, Fund. Math. 47 (1959), 57–103.

    MathSciNet  MATH  Google Scholar 

  12. H. Läuchli, A decision procedure for the weak second order theory of linear order, Contributions to mathematical logic, Proceeding of the Logic Colloquium, Hannover, 1966, North-Holland, Amsterdam, 1968.

    MATH  Google Scholar 

  13. R. McNaughton, Testing and generating infinite sequences by a finite automaton, Information and Control 9 (1966), 521–530.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. M.O. Rabin, Decidability of second-order theories and automata on infinite trees, Trans. Am. Math. Soc. 141 (1969), 1–35.

    MathSciNet  MATH  Google Scholar 

  15. D. Siefkes, Büchi's monadic second order successor arithmetic, Lecture Notes in Mathematics, vol. 120, Springer-Verlag, Berlin, 1970.

    CrossRef  MATH  Google Scholar 

  16. Th. Skolem, Untersuchungen über die Axiome des Klassenkalküls und über Produktations-und Summationsprobleme, welche gewisse Klassen von Aussagen betreffen, Skrifter, Videnskabsakademiet i Kristiania, no. 3, 1919.

    Google Scholar 

  17. S. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fu. Ma. 16 (1930), 140–150.

    MATH  Google Scholar 

  18. L. Löwenheim, Über Möglichkeiten im Relativkalkül, Fund. Math. 76 (1915), 447–470

    MATH  Google Scholar 

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© 1973 Springer-Verlag

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Büchi, J.R. (1973). 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/BFb0082721

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  • DOI: https://doi.org/10.1007/BFb0082721

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  • Print ISBN: 978-3-540-06345-2

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