Handbook of Constructive Mathematics

doi:10.1017/9781009039888

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Catren, Gabriel 2023. Abstraction, equality and univalence. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 381, Issue. 2255,

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Mandavilli, Sujay Rao 2025. Disinterring 100 New Scientific Fallacies Direct and Indirect: Using Discourse and Narrative Analyses to Unearth New Scientific Fallacies. International Journal of Innovative Science and Research Technology, p. 1961.

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Kirst, Dominik and Zeng, Haoyi 2025. The Blurred Drinker Paradox: Constructive Reverse Mathematics of the Downward Löwenheim-Skolem Theorem. p. 926.

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Bentzen, Bruno 2025. Rethinking Intuition in Constructive Mathematics. Theoria, Vol. 91, Issue. 5,

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Berger, J Bridges, Douglas Diener, Hannes and Schwichtenberg, Helmet 2025. Constructive aspects of Riemann’s permutation theorem for series. Logic Journal of the IGPL, Vol. 33, Issue. 1, p. 49.

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Edited by Douglas Bridges, University of Canterbury, Christchurch, New Zealand, Hajime Ishihara, Japan Advanced Institute of Science and Technology, Michael Rathjen, University of Leeds, Helmut Schwichtenberg, Ludwig-Maximilians-Universität Munchen

Publisher:: Cambridge University Press
Online publication date:: May 2023
Print publication year:: 2023
Online ISBN:: 9781009039888
DOI:: https://doi.org/10.1017/9781009039888

Subjects:: Mathematics (general), Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
Series:: Encyclopedia of Mathematics and its Applications

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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.

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