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Self-verifying axiom systems

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Book cover Computational Logic and Proof Theory (KGC 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 713))

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Abstract

We introduce a class of First Order axiom systems which can simultaneously verify their own consistency and prove more Π1 theorems than Peano Arithmetic. Despite these strengths, our axiom systems do not violate Godel's Incompleteness Theorem because they treat multiplication as a partial function.

Partially funded by NSF 9060509.

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Author information

Author notes

  1. E. Dan Willard

    Present address: CS Department, SUNYA, 12222, Albany, NY

Authors and Affiliations

  1. University at Albany, USA

    E. Dan Willard

Authors
  1. E. Dan Willard
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Editor information

Georg Gottlob Alexander Leitsch Daniele Mundici

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© 1993 Springer-Verlag Berlin Heidelberg

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Dan Willard, E. (1993). Self-verifying axiom systems. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1993. Lecture Notes in Computer Science, vol 713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022580

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  • DOI: https://doi.org/10.1007/BFb0022580

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57184-1

  • Online ISBN: 978-3-540-47943-7

  • eBook Packages: Springer Book Archive

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