Set theory, arithmetic, and foundations of mathematics : theorems, philosophies

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 OMEGA conjecture W. Hugh Woodin 4. omega-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 2.