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Essays in Constructive Mathematicsby Harold M. Edwards
Springer 2005; US$ 89.95This book aims to promote constructive mathematics not by defining it or formalizing it but by practicing it. This means that its definitions and proofs use finite algorithms, not `algorithms' that require surveying an infinite number of possibilities to determine whether a given condition is met. The topics covered derive from classic works of nineteenth century mathematics---among them Galois' theory of algebraic equations, Gauss's theory of binary quadratic forms and Abel's theorem about integrals of rational differentials on algebraic curves. It is not surprising that the first two topics can be treated constructively---although the constructive treatments shed a surprising amount of light on them---but the last topic, involving... more...
Constructive Negations and Paraconsistencyby Sergei P. Odintsov
Springer 2008; US$ 209.00This book presents the author's recent investigations of the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity (L.E.J. Brouwer) and the strong negation (D. Nelson) are studied in the setting of paraconsistent logic.The paraconsistent logics are those, which admit inconsistent but non-trivial theories, i.e., the logics which allow making inferences in non-trivial fashion from an inconsistent set of hypotheses. Logics in which all inconsistent theories are trivial are called explosive. In the intuitionistic logic Li, the negation is defined as reduction to absurdity. The concept of strong negation is realized in the Nelson logic N3. Both logics are explosive and have paraconsistent analogs:... more...
Bounded Arithmetic, Propositional Logic and Complexity Theoryby Jan Krajicek
Cambridge University Press 1995; US$ 126.00Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems. more...
Apartness and Uniformityby D. S. Bridges; Luminita Simona Vīta
Springer 2011; US$ 99.00This book presents a theory of apartness encompassing both point-set topology and the theory of uniform spaces. The first book on the apartness approach to constructive topology, it is a valuable addition to the literature on topology in computer science. more...
Varieties of Constructive Mathematicsby Douglas Bridges; Fred Richman
Cambridge University Press 1987; US$ 42.00This is an introduction to, and survey of, the constructive approaches to pure mathematics. more...
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