This book collects most of the invited papers presented at the 12th International Congress of Logic, Methodology and Philosophy of Science in Oviedo, August 2003. It contains state of the art accounts of ongoing work by a selection of the most renowned researchers in the field. The papers in the Logic section deal with topics in mathematical logic, as well as philosophical logic, and the area of logic and computation. The section on General Methodology contains articles on models, theories, probability, induction, causation, and other topics. A number of papers discuss Philosophical Issues of...

People have always been interested in numbers, in particular the natural numbers. Of course, we all have an intuitive notion of what these numbers are. In the late 19th century mathematicians, such as Grassmann, Frege and Dedekind, gave definitions for these familiar objects. Since then the development of axiomatic schemes for arithmetic have played a fundamental role in a logical understanding of mathematics. There has been a need for some time for a monograph on the metamathematics of first-order arithmetic. The aim of the book by Hajek and Pudlak is to cover some of the most important...