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A new concept of predicative truth and definability

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Abstract

In this paper a conception of predicative truth in the language of naive analysis is given, and the peculiarities of the induced logic are studied. It is shown that this concept can be formalized in a system with a constructive Carnap rule and that in a theory based on this concept of truth the same things can be expressed that can be expressed in the usual theories of hyperarithmetic and ramified analysis.

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Literature cited

  1. S. Feferman, “Systems of predicative analysis,” J. of Symbolic Logic,29, 1–30 (1964).

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  2. S. C. Kleene, “Hierarchies of number-theoretical predicates,” Bull. Am. Math. Soc.,61, 193–213 (1955).

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  3. S. C. Kleene, Introduction to Metamathematics, Van Nostrand (1952).

  4. P. Lorenzen, Einfuhrung in die operative Logik und Mathematik, Berlin-Heidelberg-New York (1955).

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Authors
  1. N. N. Nepeivoda
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Additional information

Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 735–745, May, 1973.

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Nepeivoda, N.N. A new concept of predicative truth and definability. Mathematical Notes of the Academy of Sciences of the USSR 13, 439–445 (1973). https://doi.org/10.1007/BF01147475

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  • DOI: https://doi.org/10.1007/BF01147475

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