Varieties Of Constructive Mathematics
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Varieties Of Constructive Mathematics
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Author : Douglas Bridges
language : en
Publisher: Cambridge University Press
Release Date : 1987-04-24
Varieties Of Constructive Mathematics written by Douglas Bridges and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-04-24 with Mathematics categories.
A survey of constructive approaches to pure mathematics emphasizing the viewpoint of Errett Bishop's school. Considers intuitionism, Russian constructivism, and recursive analysis, with comparisons among the various approaches included where appropriate.
Varieties Of Constructive Mathematics
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Author : Douglas S. Bridges
language : en
Publisher:
Release Date : 2014-05-14
Varieties Of Constructive Mathematics written by Douglas S. Bridges and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.
From Sets And Types To Topology And Analysis
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Author : Laura Crosilla
language : en
Publisher: Clarendon Press
Release Date : 2005-10-06
From Sets And Types To Topology And Analysis written by Laura Crosilla and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-06 with Mathematics categories.
This edited collection bridges the foundations and practice of constructive mathematics and focusses on the contrast between the theoretical developments, which have been most useful for computer science (eg constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logicians, mathematicians, philosophers and computer scientists Including, with contributions from leading researchers, it is up-to-date, highly topical and broad in scope. This is the latest volume in the Oxford Logic Guides, which also includes: 41. J.M. Dunn and G. Hardegree: Algebraic Methods in Philosophical Logic 42. H. Rott: Change, Choice and Inference: A study of belief revision and nonmonotoic reasoning 43. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 1 44. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 2 45. David J. Pym and Eike Ritter: Reductive Logic and Proof Search: Proof theory, semantics and control 46. D.M. Gabbay and L. Maksimova: Interpolation and Definability: Modal and Intuitionistic Logics 47. John L. Bell: Set Theory: Boolean-valued models and independence proofs, third edition
Foundational Theories Of Classical And Constructive Mathematics
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Author : Giovanni Sommaruga
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-24
Foundational Theories Of Classical And Constructive Mathematics written by Giovanni Sommaruga and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-24 with Mathematics categories.
The book "Foundational Theories of Classical and Constructive Mathematics" is a book on the classical topic of foundations of mathematics. Its originality resides mainly in its treating at the same time foundations of classical and foundations of constructive mathematics. This confrontation of two kinds of foundations contributes to answering questions such as: Are foundations/foundational theories of classical mathematics of a different nature compared to those of constructive mathematics? Do they play the same role for the resp. mathematics? Are there connections between the two kinds of foundational theories? etc. The confrontation and comparison is often implicit and sometimes explicit. Its great advantage is to extend the traditional discussion of the foundations of mathematics and to render it at the same time more subtle and more differentiated. Another important aspect of the book is that some of its contributions are of a more philosophical, others of a more technical nature. This double face is emphasized, since foundations of mathematics is an eminent topic in the philosophy of mathematics: hence both sides of this discipline ought to be and are being paid due to.
Essays In Constructive Mathematics
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Author : Harold M. Edwards
language : en
Publisher: Springer Nature
Release Date : 2022-09-29
Essays In Constructive Mathematics written by Harold M. Edwards and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-29 with Mathematics categories.
Contents and treatment are fresh and very different from the standard treatments Presents a fully constructive version of what it means to do algebra The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader
Foundations Of Constructive Mathematics
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Author : M.J. Beeson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Foundations Of Constructive Mathematics written by M.J. Beeson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connec tions with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Con structive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind.
Techniques Of Constructive Analysis
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Author : Douglas S. Bridges
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-30
Techniques Of Constructive Analysis written by Douglas S. Bridges and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-30 with Mathematics categories.
This book is an introduction to constructive mathematics with an emphasis on techniques and results obtained in the last twenty years. The text covers fundamental theory of the real line and metric spaces, focusing on locatedness in normed spaces and with associated results about operators and their adjoints on a Hilbert space. The first appendix gathers together some basic notions about sets and orders, the second gives the axioms for intuitionistic logic. No background in intuitionistic logic or constructive analysis is needed in order to read the book, but some familiarity with the classical theories of metric, normed and Hilbert spaces is necessary.
Handbook Of Constructive Mathematics
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Author : Douglas Bridges
language : en
Publisher: Cambridge University Press
Release Date : 2023-03-31
Handbook Of Constructive Mathematics written by Douglas Bridges and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-31 with Mathematics categories.
Gives a complete overview of modern constructive mathematics and its applications through surveys by leading experts.
Constructivism In Mathematics Vol 1
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Author : A.S. Troelstra
language : en
Publisher: Elsevier
Release Date : 1988-07-01
Constructivism In Mathematics Vol 1 written by A.S. Troelstra and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-07-01 with Computers categories.
These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature.
Studies In Constructive Mathematics And Mathematical Logic
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Author : A. O. Slisenko
language : en
Publisher: Springer
Release Date : 2014-01-11
Studies In Constructive Mathematics And Mathematical Logic written by A. O. Slisenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-11 with Science categories.