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First-order logic and its extensions

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⊨ISILC Logic Conference

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 499))

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References

  1. Baldwin, J.T., Blass, A.R., Glass, A.M., Kueker, D.W.: A note on the elementary theory of finite abelian groups, Algebra universalis 3 (1973), 156–159.

    Article  MathSciNet  Google Scholar 

  2. Barwise, K.J.: Axioms for abstract model theory, Annals of math. logic. (1974)

    Google Scholar 

  3. Barwise, K.J.: Back and forth thru infinitary logics, in: MAA-Studies in Mathematics 8 (1973), 5–34.

    Google Scholar 

  4. Barwise, K.J.: Absolute logic and L∞ω, Annals of Math. Logic 4 (1972), 309–340.

    Article  MATH  MathSciNet  Google Scholar 

  5. Barwise, K.J.: The Hanf number of second order logic, Jour. Symb. Logic 37 (1972), 588–594.

    Article  MATH  MathSciNet  Google Scholar 

  6. Barwise, K.J.: Infinitary logic and admissible sets, Doctoral Dissertation, Stanford (1967).

    Google Scholar 

  7. Barwise, K.J.—Kunen, K.: Hanf numbers for fragments of L + ηω, Israel J. Math. 10 (1971), 306–320.

    MATH  MathSciNet  Google Scholar 

  8. Chang, C.C.: Some remarks on the model theory of infinitary languages, in: The Syntax and Semantics of Infinitary languages, Berlin (1968), 36–63.

    Google Scholar 

  9. Chang, C.C.—Keisler, H.J.: Model theory, Amsterdam (1974).

    Google Scholar 

  10. Craig, W.—Vaught, R.L.: Finite axiomatizability using additional predicats, Jour. Symb. Logic 23 (1958), 289–308.

    Article  MathSciNet  Google Scholar 

  11. Deißler, R.: Untersuchungen über Minimalmodelle, Dissertation, Univ. of Freiburg (1974).

    Google Scholar 

  12. Erdös, P.—Rado, R.: A partition calculus in set theory, Bull. Amer. Math. Soc. 62 (1956), 427–489.

    Article  MATH  MathSciNet  Google Scholar 

  13. Feferman, S.: Infinitary properties, local functors and systems of ordinal functions, in: Conference in Mathematical Logic-London 1970, Berlin (1972), 63–97.

    Google Scholar 

  14. Feferman, S.: Two notes on abstract model theory I. Properties invariant on the range of definable relations between structures, Fund. Math. 82 (1974), 153–164.

    MATH  Google Scholar 

  15. Feferman, S.: Applications of many-sorted interpolation theorems, to appear in: Proceedings of the Tarski Symposium.

    Google Scholar 

  16. Feferman, S.: Lectures on proof theory, in: Proceedings of the Summer School in Logic, Leeds 1967, Berlin (1968), 1–107.

    Google Scholar 

  17. Flum, J.: Hanf numbers and well-ordering numbers, Arch. Math. Logic 15 (1972), 164–178.

    Article  MATH  MathSciNet  Google Scholar 

  18. Fraïssé, R.: Sur quelques classifications des systèmes de relations, Publ. Sci. Univ. Alger Ser. A 1, 35–182.

    Google Scholar 

  19. Fuhrken, G.: Skolem-type normal forms for first-order languages with a generalized quantifier, Fund. Math. 54 (1964), 291–302.

    MATH  MathSciNet  Google Scholar 

  20. Hanf, W.: Incompleteness in languages with infinitely long expressions, Fund. Math. 53 (1964), 303–323.

    Google Scholar 

  21. Hintikka, J.: Distributive normal forms in first-order logic, in: Formal systems and recursive functions, Amsterdam (1965), 48–91.

    Google Scholar 

  22. Karp, C.: Finite quantifier equivalence, in: The Theory of Models, Amsterdam (1965), 407–412.

    Google Scholar 

  23. Keisler, H. J.: Model theory for infinitary logic, Amsterdam (1971).

    Google Scholar 

  24. Lindström, P.: On extensions of elementary logic, Theoria 35 (1969), 1–11.

    Article  MATH  MathSciNet  Google Scholar 

  25. Lindström, P.: On relations between structures, Theoria 32 (1966), 172–185.

    Article  MathSciNet  Google Scholar 

  26. Lindström, P.: First order predicate logic with generalized quantifiers, Theoria 32 (1966), 186–195.

    MathSciNet  Google Scholar 

  27. López-Escobar, E. G. K.: On definable well-orderings, Fund. Math. 59 (1965), 13–21.

    Google Scholar 

  28. Magidor, M.—Malitz, J.: Compact extensions of L(Q), to appear.

    Google Scholar 

  29. Makkai, M.: Svenonius sentences and Lindström's theory on preservation theorems, Fund. Math. 73 (1972), 219–233.

    MATH  MathSciNet  Google Scholar 

  30. Makkai, M.: Vaught sentences and Lindström's regular relations, in Cambridge Summer School in Mathematical Logic, Berlin (1973), 622–660.

    Google Scholar 

  31. Morley, M.: The Hanf number for ω-logic, Jour. Symb. Logic 32 (1967), 437.

    Google Scholar 

  32. Schönfeld, W.: Ehrenfeucht-Fraisse Spiel. Disjunktive Normalform und Endlichkeitssatz. Dissertation, Stuttgart (1974).

    Google Scholar 

  33. Thomas, W.: Decision problems for some extensions of successor arithmetic, to appear.

    Google Scholar 

  34. Vaught, R. L.: The Löwenheim Skolem theorem, in: Proc. of 1964 Int'l. Cong. Logic, Meth. and Phil. Sci., Amsterdam (1965), 81–89.

    Google Scholar 

  35. Vaught, R. L: Descriptive set theory in Lw1w, in Cambridge Summer School in Mathematical Logic, Berlin (1973), 574–598.

    Google Scholar 

  36. Wolf, Th.: Diplomarbeit Freiburg (1975).

    Google Scholar 

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Authors
  1. J. Flum
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Gert H. Müller Arnold Oberschelp Klaus Potthoff

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© 1975 Springer-Verlag

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Flum, J. (1975). First-order logic and its extensions. In: Müller, G.H., Oberschelp, A., Potthoff, K. (eds) ⊨ISILC Logic Conference. Lecture Notes in Mathematics, vol 499. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0079423

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  • DOI: https://doi.org/10.1007/BFb0079423

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07534-9

  • Online ISBN: 978-3-540-38022-1

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