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Set Theory, Arithmetic, and Foundations of Mathematics

Set Theory, Arithmetic, and Foundations of Mathematics
Theorems, Philosophies

$93.00 (C)

Part of Lecture Notes in Logic

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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  • Date Published: October 2011
  • availability: In stock
  • format: Hardback
  • isbn: 9781107008045

$ 93.00 (C)
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About the Authors
  • 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arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972–1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse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.

    • Distinguished contributors include Hugh Woodin, Alle Troelstra and Akihiro Kanamori
    • Includes unpublished transcripts of Sue Toledo's conversations with Gödel, and surveys the history of logic as well as cutting edge research
    • Heavily inspired by Stanley Tennenbaum's work, this volume reflects his enormous contribution to the field
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    Product details

    • Date Published: October 2011
    • format: Hardback
    • isbn: 9781107008045
    • length: 242 pages
    • dimensions: 235 x 155 x 15 mm
    • weight: 0.48kg
    • contains: 1 b/w illus.
    • availability: In stock
  • Table of 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.

  • Editors

    Juliette Kennedy, University of Helsinki
    Juliette Kennedy is a University Lecturer in the Department of Mathematics and Statistics at the University of Helsinki.

    Roman Kossak, City University of New York
    Roman Kossak is a Professor of Mathematics in the Graduate Center at the City University of New York (CUNY).

    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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