Based on a conference that was held in Tehran, Iran, this collection of papers gives emphasis to model theory and its applications to algebra and formal theories of arithmetic. Other papers address category theory, computability, modal logic, and the history of mathematical logic in Iran.

Logicism, as put forward by Bertrand Russell, was predicated on a belief that all of mathematics can be deduced from a very small number of fundamental logical principles. In Logicism Renewed, the author revisits this concept in light of advances in mathematical logic and the need for languages that can be understood by both humans and computers that require distinguishing between the intension and extension of predicates. Using Intensional Type Theory (ITT) the author provides a unified foundation for mathematics and computer science, yielding a much simpler foundation for recursion...

Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems. The book contains 24 original papers by leading researchers. These articles exhibit the exciting recent developments in reverse mathematics and subsystems of second order arithmetic.

This text is concerned with the concept that our mathematical knowledge is inexhaustible. Basic material in predicate logic, set theory and recursion theory is presented, leading to a proof of incompleteness theorems.

This volume contains the proceedings of the conference Logical Foundations of Mathematics, Computer Science, and Physics-Kurt Godel's Legacy, held in Brno, Czech Republic on the 90th anniversary of his birth. The wide and continuing importance of Godel s work in the logical foundations of mathematics, computer science, and physics is confirmed by the broad range of speakers who participated in making this gathering a scientific event.

This book is a self-contained, up-to-date introduction to simple theories and the model theory of hyperimaginaries.

This book addresses a gap in the model-theoretic understanding of valued fields that has, until now, limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory. Part one of the book is a study of stably dominated types and it begins with an introduction to the key ideas of stability theory for stably dominated types. Part two continues with an outline of some classical results in the model theory of valued fields and explores the application of stable domination to algebraically closed valued fields. The research...

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...

The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. This volume covers many areas of contemporary logic: model theory, proof theory, set theory, and computer science, as well as philosophical logic, including tutorials on cardinal arithmetic, on Pillay s conjecture, and on...

The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.