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Semantic Characterisations of Second-Order Computability over the Real Numbers

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Computer Science Logic (CSL 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2142))

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Abstract

We propose semantic characterisations of second-order computability over the reals based on σ-definability theory. Notions of computability for operators and real-valued functionals defined on the class of continuous functions are introduced via domain theory. We consider the reals with and without equality and prove theorems which connect computable operators and real-valued functionals with validity of finite σ-formulas.

This research was supported in part by the RFBR (grants N 99-01-00485, N 00-01-00810) and by the Siberian Division of RAS (a grant for young researchers, 2000)

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Author information

Authors and Affiliations

  1. Institute of Informatics Systems, Lavrent’ev pr., 6, Novosibirsk, Russia

    M. V. Korovina

  2. Institute of Mathematics, Koptug pr., 4, Novosibirsk, Russia

    O. V. Kudinov

Authors
  1. M. V. Korovina
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  2. O. V. Kudinov
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Editor information

Editors and Affiliations

  1. LSV (Ecole Normale Supérieure de Cachan and CNRS), 61, Avenue du Président Wilson, 94230, Cachan, France

    Laurent Fribourg

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Korovina, M.V., Kudinov, O.V. (2001). Semantic Characterisations of Second-Order Computability over the Real Numbers. In: Fribourg, L. (eds) Computer Science Logic. CSL 2001. Lecture Notes in Computer Science, vol 2142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44802-0_12

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  • DOI: https://doi.org/10.1007/3-540-44802-0_12

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  • Print ISBN: 978-3-540-42554-0

  • Online ISBN: 978-3-540-44802-0

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