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[ 洋図書 ] Handbook of constructive mathematics / ( Encyclopedia of mathematics and its applications ; 185 )

edited by Douglas Bridges, University of Canterbury, Hajime Ishihara, Japan Advanced Institute of Science and Technology, Michael Rathjen, University of Leeds, Helmut Schwichtenberg, Ludwig Maximilian University of Munich. -- Cambridge University Press, -- 2023. --

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ISBN 1316510867 (hardback)
ISBN13桁 9781316510865 (hardback)
無効なISBN等 9781009039888 (PDF ebook)
テキストの言語 英語                  
分類：NDC10版 410.8
本タイトル Handbook of constructive mathematics /
著者名 edited by Douglas Bridges, University of Canterbury, Hajime Ishihara, Japan Advanced Institute of Science and Technology, Michael Rathjen, University of Leeds, Helmut Schwichtenberg, Ludwig Maximilian University of Munich.
出版地・頒布地 Cambridge :
出版者・頒布者名 Cambridge University Press,
出版年・頒布年 2023.
数量 xix, 841 pages ;
大きさ 25 cm.
書誌注記 Includes bibliographical references and index.
内容注記 Part I: Introductory -- An introduction to intuitionalistic logic / Michael Rathjen -- An introduction to constructive set theory: an appetizer / Michael Rathjen -- Bishop's mathematics: a philosophical perspective / Laura Crosilla -- Part II: Algebra and geometry -- Algebra in Bishop's style: a course in constructive algebra / Henri Lombardi -- Constructive algebra: the Quillen-Suslin Theorem / Ihsen Yengui -- Constructive algebra and point-free topology / Thierry Coquand -- Constructive projective geometry / Mark Mandelkern -- Part III: Analysis -- Elements of constructive analysis / Hajime Ishihara -- Constructive functional analysis / Hajime Ishihara -- Constructive Banach algebra theory / Robin S. Havea and Douglas Bridges -- Constructive convex optimisation / Josef Berger and Gregor Svindland -- Constructive mathematical economics / Matthew Hendtlass and Douglas Bridges -- A leisurely random walk down the lane of a constructive theory of stochastic processes / Yuen-Kwok Chan -- Part IV: Topology -- Bases of pseudocompact Bishop spaces / Iosif Petrakis -- Bishop metric spaces in formal topology / Tatsuji Kawai -- Subspaces in pointfree topology: towards a new approach to measure theory / Francesco Ciraulo -- Synthetic topology / Davorin Lešnik -- Apartness on lattices and between sets / Douglas Bridges -- Part V: Logic and foundations -- Countable choice / Fred Richman -- The minimalist foundation and Bishop's constructive mathematics / Maria Emilia Maietti and Giovanni Sambin -- Identity, equality, and extensionality in explicit mathematics / Gerhard Jäger -- Inner and outer models for constructive set theories / Robert S. Lubarsky -- An introduction to constructive reverse mathematics / Hajime Ishihara -- Systems for constructive reverse mathematics / Takako Nemoto -- Brouwer's fan theorem / Josef Berger -- Part VI: Aspects of computation -- Computational aspects of Bishop's constructive mathematics / Helmut Schwichtenberg -- Application of constructive analysis in exact real arithmetic / Kenji Miyamoto -- Efficient algorithms from proofs in constructive analysis / Mark Bickford -- On the computational content of choice principles / Ulrich Brger and Monika Seisenberger.
要約、抄録、注釈等 "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."-- Publisher's website.
著者標目 Bridges, D. S. (Douglas S.), 1945-
Ishihara, Hajime.
Rathjen, Michael.
Schwichtenberg, Helmut, 1942-
団体名(副出標目) Cambridge University Press.
統一タイトル(シリーズ副出標目) Encyclopedia of mathematics and its applications ;
シリーズの巻次 185.
シリーズ名・巻次 Encyclopedia of mathematics and its applications ; 185
一般件名 Constructive mathematics.
Mathématiques constructives.
資料情報1 『Handbook of constructive mathematics /』（Encyclopedia of mathematics and its applications ; 185）　edited by Douglas Bridges, University of Canterbury, Hajime Ishihara, Japan Advanced Institute of Science and Technology, Michael Rathjen, University of Leeds, Helmut Schwichtenberg, Ludwig Maximilian University of Munich.　Cambridge University Press,　2023. （所蔵館：中央　 請求記号：F/410.8/E56/E1-185　 資料コード：7117157055）
URL https://catalog.library.metro.tokyo.lg.jp/winj/opac/switch-detail.do?lang=ja&bibid=1352060916

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