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Non-extensional type-free theories of partial operations and classifications, I

Part of the Lecture Notes in Mathematics book series (LNM,volume 500)

Keywords

  • Inductive Generation
  • Atomic Formula
  • Total Operation
  • Conservative Extension
  • Partial Operation

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Bibliography

  • [B] P. Bernays, A system of axiomatic set theory, I., J. Symbolic Logic 2 (1937) 65–77.

    MathSciNet  MATH  Google Scholar 

  • [Bℓ] S. L. Bloom, A note on the predicatively definable sets of N. N. Nepeîvoda, IBM Research Report RC 4829, #21499, May 1, 1974.

    Google Scholar 

  • [C] A. Chauvin, Théorie des objets et théorie des ensembles, Thèse, Université de Clermont-Ferrand (1974).

    Google Scholar 

  • [F] S. Feferman, A language and axioms for explicit mathematics, in Algebra and Logic (Proc. 1974 Summer Res. Inst., Monash) ed. J. N. Crossley, to appear.

    Google Scholar 

  • [Fil] F. B. Fitch, The systemof combinatory logic, J. Symbolic Logic 28 (1963) 87–97.

    CrossRef  MathSciNet  Google Scholar 

  • [Fi2] F. B. Fitch, A consistent modal set theory, (abstract), J. Symbolic Logic 31 (1966) 701.

    MathSciNet  Google Scholar 

  • [Fr] H. Friedman, Axiomatic recursive function theory, in Logic Colloquium '69, eds. Gandy and Yates, North-Holland, Amsterdam (1971) 113–137.

    CrossRef  Google Scholar 

  • [G] P. C. Gilmore, The consistency of partial set theory without extensionality, in Axiomatic Set Theory (1967 U.C.L.A. Symposium), Proc. Symposia in Pure Math. XIII, Part II, ed. T. Tech, A.M.S., Providence, 1974, 147–153.

    CrossRef  Google Scholar 

  • [H, C] G. E. Hughes and M. J. Cresswell, An Introduction to Modal Logic, Methuen, London (1968).

    MATH  Google Scholar 

  • [K] S. C. Kleene, Recursive functionals and quantifiers of finite types, I., Trans. Amer. Math. Soc. 91 (1959) 1–32.

    MathSciNet  MATH  Google Scholar 

  • [L] P. Lindström, First order logic and generalized quantifiers Theoria 32 (1966) 186–195.

    MathSciNet  MATH  Google Scholar 

  • [M] Y. N. Moschovakis, Elementary Induction on Abstract Structures, North-Holland, Amsterdam (1974).

    MATH  Google Scholar 

  • [N] N. N. Nepeîvoda, A new notion of predicative truth and definability, (in Russian), Mat. Zametki 13 (1973) 735–745. (English translation Mathematical Notes 13 (1973) 493–495.)

    MathSciNet  MATH  Google Scholar 

  • [R] B. Russell, Mathematical logic as based on the theory of types (1908), reprinted in From Frege to Gödel, ed. J. van Heijenoort, Harvard University Press, Cambridge (1967) 150–182.

    Google Scholar 

  • [S] K. Schütte, Beweistheorie, Springer, Berlin (1960).

    MATH  Google Scholar 

  • [Sc] D. Scott, Data types as lattices (lecture notes, Kiel Summer School in Logic, 1972), to appear.

    Google Scholar 

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Dedicated to Kurt Schütte on the occasion of his 65th birthday

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© 1975 Springer-Verlag

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Feferman, S. (1975). Non-extensional type-free theories of partial operations and classifications, I. In: Diller, J., Müller, G.H. (eds) ⊨ISILC Proof Theory Symposion. Lecture Notes in Mathematics, vol 500. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079548

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  • DOI: https://doi.org/10.1007/BFb0079548

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