The book consists of contributions submitted mostly by participants of the symposium on the foundations of mathematics, organized to honour Solomon Feferman, which was held at Stanford University, in December 1998. The volume is organized into four parts: Proof-theoretic analysis, Logic and computation, Applicative and self-applicative theories, and Philosophy of modern mathematical and logical thought. For example, in the first part we can find contributions concerning ordinal analysis (such as Avigad’s and Buchholz’s contributions), Simpson’s paper that treats predicative analysis, where Feferman’s system IR is compared with Friedman’s ATR0, and Friedman’s article on combinatorial finite trees. To demonstrate the variety of themes, let us mention the Fenstad contribution “Computability theory: structure and algorithms”, Rathjen’s “Explicite mathematics with monotone inductive definitions. A survey”, and Mancosu’s “On the constructivity of proofs. A debate among Behmann, Bernays, Gődel, and Kaufmann.”

Reviewer:

jmlč