Set Theory, Arithmetic, and Foundations of Mathematics

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

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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arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Godel's previously unpublished 1972-1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse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 more

Product details

  • Electronic book text | 250 pages
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 1 b/w illus.
  • 113914281X
  • 9781139142816

About Juliette Kennedy

Juliette Kennedy is a University Lecturer in the Department of Mathematics and Statistics at the University of Helsinki. Roman Kossak is a Professor of Mathematics in the Graduate Center at the City University of New York (CUNY).show more

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. Ï -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 Godel in 1972-1975 Sue Toledo; 12. Stanley Tennenbaum's Socrates Curtis Franks; 13. Tennenbaum's proof of the irrationality of â more