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

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arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972-1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse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

Juliettf Kfnnedy is a University Lecturer in the Department of Mathematics and Statistics at the University of Helsinki. She has published a number of papers on the mathematical and philosophical work of Kurt Gdel, as well as in the area of set-theoretic model theory. Her present work concerns the study of inner models from extended logics. Roman Kossak is a Professor of Mathematics in the Graduate Center at the City University of New York (CUNY). He does research on nonstandard models of Peano Arithmetic and its fragments, and is particularly interested in model theory of recursive saturation and in nonstandard satisfaction classes.