This volume commemorates the life, work and foundational views of Kurt Goedel (1906-78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Goedel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Goedel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

Cal Elgot was a very serious and thoughtful researcher, who with great determi nation attempted to find basic explanations for certain mathematical phenomena as the selection of papers in this volume well illustrate. His approach was, for the most part, rather finitist and constructivist, and he was inevitably drawn to studies of the process of computation. It seems to me that his early work on decision problems relating automata and logic, starting with his thesis under Roger Lyndon and continuing with joint work with Biichi, Wright, Copi, Rutledge, Mezei, and then later with Rabin, set the stage for his attack on the theory of computation through the abstract treatment of the notion of a machine. This is also apparent in his joint work with A. Robinson reproduced here and in his joint papers with John Shepherdson. Of course in the light of subsequent work on decision problems by Biichi, Rabin, Shelah, and many, many others, the subject has been placed on a completely different plane from what it was when Elgot left the area. But I feel that his papers, results-and style-were very definitely influential at the time and may well have altered the course of the investigation of these problems. As Sammy Eilenberg explains, the next big influence on Elgot's thinking was category theory, which gave him a way of expressing his ideas in a sharply algebraic manner. The joint book with Eilenberg is one illustration of this influence."

This volume commemorates the life, work, and foundational views of Kurt Godel (1906 1978), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency with the other widely accepted axioms of set theory of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances, and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology, and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Godel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Godel's fundamental work in mathematics, logic, philosophy, and other disciplines for future generations of researchers."