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.

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A collection of remarkable papers from various areas of mathematical logic, written by outstanding members of the field.

About the Author

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).