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arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of G?del's previously unpublished 1972-1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse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.
Author(s): Juliette Kennedy, Roman Kossak (editors)
Series: Lecture Notes in Logic
Publisher: Cambridge University Press
Year: 2011
Language: English
Pages: 242
Cover......Page 1
Review......Page 2
Series......Page 3
Title......Page 4
Copyright......Page 5
Contents......Page 8
§ 1. Introduction......Page 10
§2. Contents......Page 11
Historical Remarks on Suslin’s Problem, Akihiro Kanamori......Page 16
The Continuum Hypothesis, the Generic-Multiverse of Sets, and the Ω Conjecture, W. Hugh Woodin......Page 28
ω-Models of Finite Set Theory, Ali Enayat and Albert Visser......Page 58
Tennembaum’s Theorem for Models of Arithmetic, Richard Kaye......Page 81
Hierarchies of Subsystems of Weak Arithmetic, Shahram Mohsenipour......Page 95
Diphantine Correct Open Induction, Sidney Raffer......Page 108
Tennembaum’s Theorm and Recursive Reducts, James H. Schmerl......Page 127
History of Constructivism in the 20th Century, A.S. Troelstra......Page 165
A Very Short History of Ultrafinitism, Rose M. Cherubin and Mirco A. Mannucci......Page 195
Sue Toledo’s Notes of Her Conversations with Gödel in 1972-5, Sue Toledo......Page 215
Stanley Tennembaum’s Socrates, Curtis Franks......Page 223
Tennembaum’s Proof of the Irrationality of Square Root of 2, Jouko Vāānānen......Page 241
