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  3. Effective Mathematics of the Uncountable
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    • Publisher:
      Cambridge University Press
      Publication date:
      December 2013
      October 2013
      ISBN:
      9781139028592
      9781107014510
      DOI:
      https://doi.org/10.1017/CBO9781139028592
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.44kg, 204 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
      Series:
      Lecture Notes in Logic (41)
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    Subjects:
    Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
    Series:
    Lecture Notes in Logic (41)
    Information

    Book description

    Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods – some old, some new – that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for researchers in computability theory and related areas.

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