Handbook of Constructive Mathematics (Encyclopedia of Mathematics and its Applications)

Constructive mathematics – mathematics in which 'there exists' always means 'we can construct' – is enjoying a renaissance. fifty years on from Bishop's groundbreaking account of constructive analysis, constructive mathematics has spread out to touch almost all areas of mathematics and to have profound influence in theoretical computer science. This handbook gives the most complete overview of modern constructive mathematics, with contributions from leading specialists surveying the subject's myriad aspects. Major themes include: constructive algebra and geometry, constructive analysis, constructive topology, constructive logic and foundations of mathematics, and computational aspects of constructive mathematics. A series of introductory chapters provides graduate students and other newcomers to the subject with foundations for the surveys that follow. Edited by four of the most eminent experts in the field, this is an indispensable reference for constructive mathematicians and a fascinating vista of modern constructivism for the increasing number of researchers interested in constructive approaches.

Douglas Bridges is Professor Emeritus of Pure Mathematics at University of Canterbury, Christchurch, New Zealand. He is co-author, with the late Errett Bishop, of the monograph Constructive Analysis, as well as seven other books and almost 200 research papers in constructive mathematics.

Hajime Ishihara is Professor of Mathematical Logic at Japan Advanced Institute of Science and Technology (JAIST). He has worked for over thirty years in constructive mathematics and mathematical logic, in which he is known for introducing 'Ishihara's tricks' and for opening up constructive reverse mathematics.

Michael Rathjen was Professor of Mathematics at the Ohio State University and is currently Professor of Mathematics at the University of Leeds, England. His main research area is mathematical logic, especially proof theory, ordinal analysis, constructive and alternative set theories as well as intuitionism.

Helmut Schwichtenberg is Professor Emeritus of Mathematics at Ludwig-Maximilians-Universität, Munich, Germany. He is co-author of the monographs Basic Proof Theory (1996, 2000) and Proofs and Computations (2012).