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Philosophical Dimensions of Logic and Science pp 47–56Cite as

On Σ N -Definability in Arithmetic

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Part of the book series: Synthese Library ((SYLI,volume 320))

Abstract

Under certain assumptions, the structures K n +1(M ; X) and I n +1 (M ; X) satisfy that

$${K_{n + 1}}\left( {M;X} \right)\;\left| { = I\sum {_n + \;\neg B\sum {_{n + 1}\;and\;{I_{n + 1}}\left( {M;X} \right)\;\left| { = B\sum {_{n + 1} + \neg I\sum {_{n + 1}} } } \right.} } } \right.$$

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References

  • Clôte, P. G. (1983). Partition relations in arithmetic. Lecture Notes in Mathematics, 1130: 32–68.

    Article  Google Scholar 

  • Fernández-Margarit, A. and Pérez-Jiménez, M. J. (1994). Maximum schemes in arithmetic. Mathematical Logic Quarterly, 40: 425–430.

    Article  Google Scholar 

  • Graciani, M. C., Pérez-Jiménez, M. J., Romero, A., and Sancho, F. (2000). Initial segment maximal En-definable sets in fragments of arithmetic. The Yearbook of the Kurt Gödel Society. Forthcoming.

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  • Hâjek, P. and Pudlâk, P. (1993). Metamathematics of First-Order Arithmetic Springer Verlag.

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  • Kaye, R. (1991). Models of Peano Arithmetic, volume XV of Oxford Logic Guides. Clarendon Press, Oxford.

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  • Paris, J. and Kirby, L. (1978). En-collection schemas in arithmetic. Logic Colloquium’77, pp. 199–209.

    Google Scholar 

  • Pérez-Jiménez, M. J. (1992). Esquema,s del Mcíximo en la Aritmética. Doctoral Thesis. Universidad de Sevilla.

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Author information

Authors and Affiliations

  1. Computer Science and Artificial Intelligence, University of Seville, Spain

    J. Borrego-Diaz, A. Fernández-Margarit & M. J. Pérez-Jimenez

Authors
  1. J. Borrego-Diaz
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  2. A. Fernández-Margarit
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  3. M. J. Pérez-Jimenez
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Editor information

Editors and Affiliations

  1. The Jagiellonian University, Kraków, Poland

    Artur Rojszczak  & Jacek Cachro  & 

  2. The University of Information Technology and Management, Rzeszów, Poland

    Gabriel Kurczewski

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© 2003 Springer Science+Business Media Dordrecht

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Borrego-Diaz, J., Fernández-Margarit, A., Pérez-Jimenez, M.J. (2003). On Σ N -Definability in Arithmetic. In: Rojszczak, A., Cachro, J., Kurczewski, G. (eds) Philosophical Dimensions of Logic and Science. Synthese Library, vol 320. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2612-2_4

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  • DOI: https://doi.org/10.1007/978-94-017-2612-2_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6432-5

  • Online ISBN: 978-94-017-2612-2

  • eBook Packages: Springer Book Archive

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