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Kurt Gödel Colloquium on Computational Logic and Proof Theory

KGC 1997: Computational Logic and Proof Theory pp 233–240Cite as

Two semantics and logics based on the Gödel interpretation

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1289))

Abstract

Two arithmetic constructive theories based on Dialectica interpretation are introduced and studied in the paper. For an arithmetic formula A let A D be its Dialectica interpretation in the language of arithmetic in all finite types. The translation (A D)° of A D back into the language of first-order arithmetic using the system HRO of hereditary recursive operations is considered. The theories T1 and T2 consist of arithmetic sentences A such that (A D)° is true in the standard model and provable in the intuitionistic arithmetic respectively. Using the author's recent results on the arithmetic complexity of the predicate logics of constructive arithmetic theories it is proved that the logic of T1 is not recursively enumerable and the logic of T2 is II 2-complete.

Partially supported by RFBR grant 96-01-01470 and by INTAS-RFBR grant 95-0095.

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References

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Authors and Affiliations

  1. Department of Mathematical Logic and Theory of Algorithms, Faculty of Mechanics and Mathematics, Moscow State University, 119899, Moscow, Russia

    V. Plisko

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  1. V. Plisko
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Georg Gottlob Alexander Leitsch Daniele Mundici

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© 1997 Springer-Verlag Berlin Heidelberg

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Plisko, V. (1997). Two semantics and logics based on the Gödel interpretation. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1997. Lecture Notes in Computer Science, vol 1289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63385-5_46

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  • DOI: https://doi.org/10.1007/3-540-63385-5_46

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63385-3

  • Online ISBN: 978-3-540-69806-7

  • eBook Packages: Springer Book Archive

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