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Home > Catalog > Set Theory, Arithmetic, and Foundations of Mathematics
Set Theory, Arithmetic, and Foundations of Mathematics
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Details

  • 1 b/w illus.
  • Page extent: 242 pages
  • Size: 228 x 152 mm
  • Weight: 0.48 kg

Library of Congress

  • Dewey number: 510
  • Dewey version: 23
  • LC Classification: QA248 .S4125 2011
  • LC Subject headings:
    • Set theory
    • Logic, Symbolic and mathematical
    • Mathematics--Philosophy

Library of Congress Record

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Hardback

 (ISBN-13: 9781107008045)

In stock

$93.00 (C)

This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum's theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972–1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse view; Anne Troelstra's history of intuitionism through 1991; and Aki Kanamori's history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory, and is ideal for researchers and graduate students in mathematical logic and philosophy of mathematics.

Contents

1. Introduction Juliette Kennedy and Roman Kossak; 2. Historical remarks on Suslin's problem Akihiro Kanamori; 3. The continuum hypothesis, the generic-multiverse of sets, and the Ω conjecture W. Hugh Woodin; 4. ω-Models of finite set theory Ali Enayat, James H. Schmerl and Albert Visser; 5. Tennenbaum's theorem for models of arithmetic Richard Kaye; 6. Hierarchies of subsystems of weak arithmetic Shahram Mohsenipour; 7. Diophantine correct open induction Sidney Raffer; 8. Tennenbaum's theorem and recursive reducts James H. Schmerl; 9. History of constructivism in the 20th century A. S. Troelstra; 10. A very short history of ultrafinitism Rose M. Cherubin and Mirco A. Mannucci; 11. Sue Toledo's notes of her conversations with Gödel in 1972–1975 Sue Toledo; 12. Stanley Tennenbaum's Socrates Curtis Franks; 13. Tennenbaum's proof of the irrationality of √2.

Contributors

Juliette Kennedy, Roman Kossak, Akihiro Kanamori, W. Hugh Woodin, Ali Enayat, James H. Schmerl, Albert Visser, Richard Kaye, Shahram Mohsenipour, Sidney Raffer, A. S. Troelstra, Rose M. Cherubin, Mirco A. Mannucci, Sue Toledo, Curtis Franks

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