Reuniting The Antipodes Constructive And Nonstandard Views Of The Continuum
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Reuniting The Antipodes Constructive And Nonstandard Views Of The Continuum
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Author : Peter Schuster
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Reuniting The Antipodes Constructive And Nonstandard Views Of The Continuum written by Peter Schuster 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 2013-03-14 with Mathematics categories.
At first glance, Robinson's original form of nonstandard analysis appears nonconstructive in essence, because it makes a rather unrestricted use of classical logic and set theory and, in particular, of the axiom of choice. Recent developments, however, have given rise to the hope that the distance between constructive and nonstandard mathematics is actually much smaller than it appears. So the time was ripe for the first meeting dedicated simultaneously to both ways of doing mathematics – and to the current and future reunion of these seeming opposites. Consisting of peer-reviewed research and survey articles written on the occasion of such an event, this volume offers views of the continuum from various standpoints. Including historical and philosophical issues, the topics of the contributions range from the foundations, the practice, and the applications of constructive and nonstandard mathematics, to the interplay of these areas and the development of a unified theory.
Reuniting The Antipodes Constructive And Nonstandard Views Of The Continuum
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Author : Peter Schuster
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Reuniting The Antipodes Constructive And Nonstandard Views Of The Continuum written by Peter Schuster 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 2001 with Mathematics categories.
Symposion Proceedings, San Servolo, Venice, Italy, May 16-22, 1999
The Continuous And The Infinitesimal In Mathematics And Philosophy
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Author : John Lane Bell
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2005
The Continuous And The Infinitesimal In Mathematics And Philosophy written by John Lane Bell and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The Continuum
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Author : Rudolf Taschner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Continuum written by Rudolf Taschner 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.
"Few mathematical structures have undergone as many revlSlons or have been presented in as many guises as the real numbers. Every generation re-examines the reals in the light of its values and mathematical objectives." This citation is said to be due to Gian-Carlo Rota, and in this book its correctness again is affirmed. Here I propose to investigate the structure of the mathematical continuum by undertaking a rather unconventional access to the real numbers: the intuitionistic one. The traces can be tracked back at least to L.E.J. Brouwer and to H. Weyl. Largely unknown photographies of Weyl in Switzerland after World War II provided by Peter Bettschart enliven the abstract text full of subtle definitions and sophisticated estimations. The book can be read by students who have undertaken the usual analysis courses and want to know more about the intrinsic details of the underlying concepts, and it can also be used by university teachers in lectures for advanced undergraduates and inseminaries for graduate students. I wish to thank Walter Lummerding and Gottfried Oehl who helped me with their impressive expert knowledge of the English language. I also take the opportunity to express my gratitude to Ulrike Schmickler-Hirzebruch and to the staff of Vieweg-Verlag for editing my manuscript just now, exactly 50 years after the death of Hermann Weyl, in their renowned publishing house. Vienna, 2005 Rudolf Taschner Contents 1 Introduction and historical remarks 1 1.1 F AREY fractions. .
Logic And Its Applications
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Author : Andreas Blass
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Logic And Its Applications written by Andreas Blass and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Two conferences, Logic and Its Applications in Algebra and Geometry and Combinatorial Set Theory, Excellent Classes, and Schanuel Conjecture, were held at the University of Michigan (Ann Arbor). These events brought together model theorists and set theorists working in these areas. This volume is the result of those meetings. It is suitable for graduate students and researchers working in mathematical logic.
Structural Proof Theory
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Author : Sara Negri
language : en
Publisher: Cambridge University Press
Release Date : 2008-07-10
Structural Proof Theory written by Sara Negri 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 2008-07-10 with Mathematics categories.
A concise introduction to structural proof theory, a branch of logic studying the general structure of logical and mathematical proofs.
Mathematical Foundations Of Computer Science 2013
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Author : Krishnendu Chatterjee
language : en
Publisher: Springer
Release Date : 2013-08-16
Mathematical Foundations Of Computer Science 2013 written by Krishnendu Chatterjee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-16 with Computers categories.
This book constitutes the thoroughly refereed conference proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013, held in Klosterneuburg, Austria, in August 2013. The 67 revised full papers presented together with six invited talks were carefully selected from 191 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, databases and knowledge-based systems, foundations of computing, logic in computer science, models of computation, semantics and verification of programs, and theoretical issues in artificial intelligence.
Exogenous Factors In Colonic Carcinogenesis
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Author : W. Scheppach
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-31
Exogenous Factors In Colonic Carcinogenesis written by W. Scheppach 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 2003-01-31 with Medical categories.
This book is the proceedings of Falk Symposium 128, held in Würzburg, Germany, on May 2-3, 2002, and dedicated to the important issue of colonic carcinogenesis and its underlying genetic and environmental factors. Colorectal cancer is one of the leading causes of cancer-related death in industrialized countries. It has been recognized to be the consequence of a dynamic process leading from hyperproliferative epithelium through different classes of adenomas to invasive carcinoma. This adenoma-carcinoma sequence has been characterized on a molecular basis. Modern molecular biology has also helped to clarify the clustering of colorectal cancer within families, a phenomenon that has been known to clinicians for a long time. Thus, the pathogenesis of the two distinct familial colon cancer syndromes FAP (familial adenomatous polyposis) and HNPCC (hereditary non-polyposis colorectal cancer) is increasingly being understood. Thereby, an identification of affected people has become possible before the disease has manifested. There is also convincing evidence that the pathogenesis of sporadic colonic cancer is modulated by environmental, mainly nutritional, factors. Carcinogens seem to be far less important than the components of the `normal' human diet. It is likely that the interplay between protective and noxious dietary compounds determines the progression of the adenoma-carcinoma sequence. Additionally, a broad spectrum of drugs has been shown to affect colonic tumorigenesis, which provides the rationale for chemoprevention strategies. These issues set the scene for discussions on how genetic and environmental factors may interact in the pathogenesis of colonic cancer, contributing fresh ideas to the prevention of this most prevalent malignancy in the industrialized world.
Scientific Progress
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Author : Craig Dilworth
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-18
Scientific Progress written by Craig Dilworth 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 2007-09-18 with Science categories.
Kuhn and Feyerabend formulated the problem, Dilworth provides the solution. In the fourth edition of this highly original book, Craig Dilworth answers the questions raised by the incommensurability thesis. Logical empiricism cannot account for theory conflict. Popperianism cannot account for how one theory is a progression beyond another. Dilworth’s Perspectivist conception of science covers both bases with a concept of scientific progress based on both rationalism and empiricism.
Mathesis Universalis Computability And Proof
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Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2019-10-25
Mathesis Universalis Computability And Proof written by Stefania Centrone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-25 with Philosophy categories.
In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gründe”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.