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Kurt Godel (1906 1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Godel s centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Godel s writings are among the topics covered. Several chapters discuss his intellectual development...

Kurt Godel (1906 1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Godel s centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Godel s writings are among the topics covered. Several chapters discuss his intellectual development...

In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom provided by Cantorian set theory was purchased at a heavy...

Grigori Mints is one the most distinguished proof theorists of our time. He has contributed significantly not only to the subject in general but also to most of its applications. This collection of papers by a number of Mints' colleagues worldwide are both a personal tribute and a testimony to his breadth and importance by dealing with all areas in which Mints has worked: from proof-theoretical reductions through non-classical logics and category theory to automated theorem proving and proof mining, i.e., the extraction of mathematical information from formal proofs. The collection itself is...