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A note on three-valued logic and Tarski theorem on truth definitions

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Abstract

We introduce a notion of semantical closure for theories by formalizing Nepeivoda notion of truth. [10]. Tarski theorem on truth definitions is discussed in the light of Kleene's three valued logic (here treated with a formal reinterpretation of logical constants). Connections with Definability Theory are also established.

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References

  1. W. Ackermann,Widerspruchfreieraufbau einer typenfreier Logik,Mathematische Zeitschrift, 55 (1952) pp. 364–84, 57 (1953), pp. 155–66.

    Google Scholar 

  2. P. Aczel,An introduction to inductive definitions, in: J. Barwise (editor), Handbook of Mathematical Logic, North-Holland, Amsterdam 1977, pp. 739–82.

    Google Scholar 

  3. S. Feferman,Non-extensional type-free theories of partial operations and classifications I, in: J. Diller-G.H. Müller (editors),Proof Theory Symposium Kiel 1974, Lecture Notes in Mathematics, vol. 500, Springer, Berlin 1974, pp. 73–118.

    Google Scholar 

  4. F. Fitch,An extension of basic logic,Journal of Symbolic Logic 13 (1948), pp. 95–106.

    Google Scholar 

  5. P. Gilmore,The consistency of partial set theory without extensionality, in: T. Jech (editor),Axiomatic Set Theory II Proceedings of Symposia in Pure Mathematics, vol. 13, Part II, Providence R.I., 1974, pp. 147–153.

  6. S. Kleene,Introduction to Metamathematics, Van Nostrand-Reinhold, Princeton 1952.

    Google Scholar 

  7. S. Kripke,Outline of a theory of truth,Journal of Philosophy 72 (1975), pp. 690–716.

    Google Scholar 

  8. Y. Moschovakis,Abstract First Order Computability II,Transactions of the American Mathematical Society 138 (1969), pp. 465–504.

    Google Scholar 

  9. —,Elementary Induction on abstract structures, North-Holland, Amsterdam 1976.

    Google Scholar 

  10. N. Nepeivoda,A new notion of predicative truth and definability, English translation in:Mathematical Notes 13 (1973), pp. 439–444.

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut, Ludwig-Maximilians Universität, München, West Germany

    Andrea Cantini

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  1. Andrea Cantini
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A first version was prepared for sec. 5-Gnsaga-CNR and presented at the Logic Seminar, Institute of Philosophy, University of Firenze, in the academic year 1978–79. The author would like to thank the referee for his criticism and the Alexander von Humboldt-Stiftung for the support during the revision of the paper.

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Cantini, A. A note on three-valued logic and Tarski theorem on truth definitions. Stud Logica 39, 405–414 (1980). https://doi.org/10.1007/BF00713550

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  • DOI: https://doi.org/10.1007/BF00713550

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