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A Note on the Proof-Theoretic Strength of a Single Application of the Schema of Identity

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Proof Theory in Computer Science (PTCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2183))

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Abstract

Every instance of the schema of identity is derivable from identity axioms. However, from a proof theoretic perspective the schema of identity is quite powerful. Even one instance of it can be used to prove formulas uniformly where no fixed number of instances of identity axioms is sufficient for this purpose.

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References

  1. [Baaz, M. and Leitsch, A., 1994]On Skolemization and Proof Complexity. Fundamenta Informaticae 20(4), pages 353–379.

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  2. [Baaz, M. and Leitsch, A., 1999]Cut normal forms and proof complexity. Ann. Pure Appl. Logic 97(1-3), pages 127–177.

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  3. [Baaz, M. and Pudlák, P., 1993]Kreisel’s conjecture for L.1. In P. Clote and J. Krajíček, editors, Arithmetic, Proof Theory and Computational Complexity, pages 29–59. Oxford University Press, 1993. With a postscript by G. Kreisel.

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  4. [Leitsch, A., 1997]The Resolution Calculus. Springer-Verlag, Berlin, Heidelberg, New York.

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  5. [Takeuti, G., 1980]Proof Theory. North-Holland, Amsterdam, 2nd edition.

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  6. [Yukami, T., 1984]Some results on speed-up. Ann. Japan Assoc. Philos. Sci., 6, pages 195–205.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Algebra und Computermathematik E118.2, Technische Universität Wien, A-1040, Vienna, Austria

    Matthias Baaz

  2. Institut für Computersprachen E185, Technische Universität Wien, A-1040, Vienna, Austria

    Christian G. Fermüller

Authors
  1. Matthias Baaz
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  2. Christian G. Fermüller
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Editor information

Editors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, 72076, Tübingen, Germany

    Reinhard Kahle  & Peter Schroeder-Heister  & 

  2. Theoretische Informatik, ETH Zürich, ETH Zentrum, 8092, Zürich, Switzerland

    Robert Stärk

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© 2001 Springer-Verlag Berlin Heidelberg

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Baaz, M., Fermüller, C.G. (2001). A Note on the Proof-Theoretic Strength of a Single Application of the Schema of Identity. In: Kahle, R., Schroeder-Heister, P., Stärk, R. (eds) Proof Theory in Computer Science. PTCS 2001. Lecture Notes in Computer Science, vol 2183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45504-3_3

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  • DOI: https://doi.org/10.1007/3-540-45504-3_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42752-0

  • Online ISBN: 978-3-540-45504-2

  • eBook Packages: Springer Book Archive

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