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  3. Subsystems of Second Order Arithmetic
  • Cited by 418
      • 2nd edition
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    • Publisher:
      Cambridge University Press
      Publication date:
      February 2010
      May 2009
      ISBN:
      9780511581007
      9780521884396
      9780521150149
      DOI:
      https://doi.org/10.1017/CBO9780511581007
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.8kg, 464 Pages
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.65kg, 464 Pages
      • Subjects:
      Mathematics, Logic, Categories and Sets, Programming Languages and Applied Logic
      Series:
      Perspectives in Logic
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    • Selected: Digital
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    Subjects:
    Mathematics, Logic, Categories and Sets, Programming Languages and Applied Logic
    Series:
    Perspectives in Logic
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    Book description

    Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic.

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