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The Syntax and Semantics of Infinitary Languages pp 139–151Cite as

Choice of infinitary languages by means of definability criteria; Generalized recursion theory

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 72))

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Bibliography

  1. Barwise, J., Thesis, Stanford University (1967).

    Google Scholar 

  2. Craig, W., Satisfaction for nth order language defined in nth order, JSL 30 (1965), 13–21, reviewed MR 33 (1967), 659–660, #3883.

    MathSciNet  Google Scholar 

  3. Feferman, S., Persistent and invariant formulas for outer extensions, Compositio 20 (1968).

    Google Scholar 

  4. Fraissé, R., Une notion de récursivité relative, pp. 323–328 in: Infinitistic Methods, Warsaw, 1961.

    Google Scholar 

  5. Gödel, K., Remarks before the Princeton Bicentennial Conference on problems in mathematics, pp. 84–88 in: The Undecidable, ed. M. Davis, N.Y., 1955.

    Google Scholar 

  6. Grzegorezyk, A., A. Mostowski, and S. Ryll-Nardzewski, The classical and ω-complete arithmetic, JSL 23 (1958), 188–206.

    MathSciNet  Google Scholar 

  7. Hanf, W., Incompactness in languages with infinitely long expressions, F.M. 53 (1964), 309–324.

    MathSciNet  MATH  Google Scholar 

  8. Karp, C.R., Languages with expressions of infinite length, Amsterdam (1964).

    Google Scholar 

  9. -, Primitive recursive set functions: a formulation with applications to infinitary formal systems, JSL 31 (1966), 294.

    Google Scholar 

  10. Kleene, S. C., Recursive functionals and quantifiers of finite types, Trans. Amer. Math. Soc. 91 (1959), 1–52.

    MathSciNet  MATH  Google Scholar 

  11. Kreisel, G., Set theoretic problems suggested by the notion of potential totality, Proceedings of the Symposium on Infinitistic Methods in the Foundations of Mathematics, Warsaw, Sept. 2–8, 1959 (1961), 103–140.

    Google Scholar 

  12. Kreisel, G., Model-theoretic invariants; applications to recursive and hyperarithmetic operations, The theory of Models (1965), 190–205.

    Google Scholar 

  13. Kreisel, G., Mathematical Logic, in Lectures on modern mathematics, vol. III, ed. Saaty (1965), 95–195.

    Google Scholar 

  14. Kreisel, G., Informal rigour and completeness proofs, pp. 138–171 of: Problems in the Philosophy of Mathematics, Amsterdam, (1967).

    Google Scholar 

  15. Kreisel, G., and J. L. Krivine, Elements of mathematical logic; theory of models, North Holland Publishing Co., (1967).

    Google Scholar 

  16. Kripke, S., Transfinite recursions on admissible ordinals I, II, JSL, 29 (1964), 161–162.

    Google Scholar 

  17. Kunen, K., Implicit definability and infinitary languages, JSL 33 (1968).

    Google Scholar 

  18. Lacombe, D., Deux généralisations de la notion de récursivité, C. R. Acad. Sc. Paris 258 (1964), 3141–3143 and 3410–3413.

    MathSciNet  MATH  Google Scholar 

  19. Levy, A., A hierarchy of formulas in set theory, Memoirs of the Amer. Math. Soc. 57 (1965).

    Google Scholar 

  20. Malitz, J. I., Thesis, University of California, Berkeley 1966.

    Google Scholar 

  21. Mostowski, A., On a generalization of quantifiers, F.M. 44 (1957), 12–36.

    MathSciNet  MATH  Google Scholar 

  22. -, Representability of sets in formal systems, Recursive function theory, Proc. Symposia in Pure Mathematics, 5 (1962), 29–48.

    Article  MathSciNet  Google Scholar 

  23. Scott, D. S., Logic with denumerably long formulas and finite strings of quantifiers, pp. 329–341 of Theory of Models, Amsterdam, 1965.

    Google Scholar 

  24. Vaught, R. L., Sentences true in all constructive models, JSL 24 (1959), 1–15.

    Google Scholar 

  25. -, The completeness theorem of logic with the added quantifier ‘there are uncountably many' F.M. 54 (1964), 303–304.

    MathSciNet  MATH  Google Scholar 

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Authors
  1. G. Kreisel
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Jon Barwise

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© 1968 Springer-Verlag

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Kreisel, G. (1968). Choice of infinitary languages by means of definability criteria; Generalized recursion theory. In: Barwise, J. (eds) The Syntax and Semantics of Infinitary Languages. Lecture Notes in Mathematics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079687

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  • DOI: https://doi.org/10.1007/BFb0079687

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04242-6

  • Online ISBN: 978-3-540-35900-5

  • eBook Packages: Springer Book Archive

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