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Semantical Completeness of First-Order Predicate Logic and the Weak Fan Theorem

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Abstract

Within a weak system \({{{\sf WKVS}}}\) of intuitionistic analysis one may prove, using the Weak Fan Theorem as an additional axiom, a completeness theorem for intuitionistic first-order predicate logic relative to validity in generalized Beth models as well as a completeness theorem for classical first-order predicate logic relative to validity in intuitionistic structures. Conversely, each of these theorems implies over \({{{\sf WKVS}}}\) the Weak Fan Theorem.

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References

  1. Kreisel G., Troelstra A.S.: Formal systems for some branches of intuitionistic analysis. Annals of Mathematical Logic 1, 229–387 (1970)

    Article  Google Scholar 

  2. Krivtsov V. N.: An intuitionistic completeness theorem for classical predicate logic. Studia Logica 86(1), 109–115 (2010)

    Article  Google Scholar 

  3. Loeb I.: Equivalents of the (Weak) Fan Theorem. Annals of Pure and Applied Logic 132, 51–66 (2005)

    Article  Google Scholar 

  4. de Swart H.C.M.: Another intuitionistic completeness proof. Journal of Symbolic Logic 41, 644–662 (1976)

    Article  Google Scholar 

  5. Troelstra, A. S., and D. van Dalen, Constructivism in Mathematics, vol. II, North-Holland, Amsterdam, 1988.

  6. Veldman W.: An intuitionistic completeness theorem for intuitionistic predicate logic. Journal of Symbolic Logic 41, 159–166 (1976)

    Google Scholar 

  7. Veldman, W., Brouwer’s approximate fixed-point theorem is equivalent to Brouwer’s fan theorem, in S. Lindström et al., (eds.), Logicism, Intuitionism, and Formalism, vol. 341 of Synthese Library, Springer, New York, 2009, pp. 277–299.

  8. Veldman, W., Brouwer’s fan theorem as an axiom and as a contrast to Kleene’s alternative, arXiv:1106.2738, 2011 (submitted to Archive for Mathematical Logic).

  9. Veldman, W., Some further equivalents of Brouwer’s fan theorem and of Kleene’s alternative, arXiv:1311.6988, 2013 (submitted to Annals of Pure and Applied Logic).

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Authors and Affiliations

  1. Department of Mathematical Logic and Theory of Algorithms, Faculty of Mechanics and Mathematics, Moscow State University, Vorob’evy Gory, 119991, Moscow, Russian Federation

    Victor N. Krivtsov

  2. Faculty of Applied Mathematics, Moscow State University of Psychology and Education, Sretenka, 29, 127051, Moscow, Russian Federation

    Victor N. Krivtsov

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  1. Victor N. Krivtsov
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Correspondence to Victor N. Krivtsov.

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Krivtsov, V.N. Semantical Completeness of First-Order Predicate Logic and the Weak Fan Theorem. Stud Logica 103, 623–638 (2015). https://doi.org/10.1007/s11225-014-9582-z

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  • DOI: https://doi.org/10.1007/s11225-014-9582-z

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