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Author: Michael Hallett
Publisher: Oxford University Press
ISBN: 9780198532835
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Author: Michael Hallett
Publisher: Oxford University Press
ISBN: 9780198532835
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Author: Michael Hallett
Publisher: Oxford University Press, USA
ISBN:
Category : Business & Economics
Languages : en
Pages : 376
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Book Description
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Author: Moshe Machover
Publisher: Cambridge University Press
ISBN: 9780521479981
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.
Author: Mary Tiles
Publisher: Courier Corporation
ISBN: 0486138550
Category : Mathematics
Languages : en
Pages : 258
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Book Description
DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div
Author: Stephen Pollard
Publisher: Courier Dover Publications
ISBN: 0486805824
Category : Mathematics
Languages : en
Pages : 196
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Book Description
This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.
Author: John P. Mayberry
Publisher: Cambridge University Press
ISBN: 9780521770347
Category : Mathematics
Languages : en
Pages : 454
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Book Description
This book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. The author investigates the logic of quantification over the universe of sets and discusses its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. Suitable for graduate students and researchers in both philosophy and mathematics.
Author: Andrea Asperti
Publisher: Springer
ISBN: 3540278184
Category : Computers
Languages : en
Pages : 402
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Book Description
The International Conference on Mathematical Knowledge Management has now reached its third edition, creating and establishing an original and stimulating scientific community transversal to many different fields and research topics. The broad goal of MKM is the exploration of innovative, semantically enriched, digital encodings of mathematical information, and the study of new services and tools exploiting the machine-understandable nature of the information. MKM is naturally located in the border area between digital libraries and the mec- nization of mathematics, devoting a particular interest to the new developments in information technology, and fostering their application to the realm of ma- ematical information. The conference is meant to be a forum for presenting, discussing and comparing new tools and systems, standardization e?orts, critical surveys, large experiments,and case studies. At present, we are still getting to know each other, to understand the work done by other people, and the potentialities offered by their work to our own research activity. However, the conference is rapidly acquiring scienti?c strength and academic interest, attracting more and more people and research groups, and offering a challenging alternative to older, more conservative conferences. July 2004 Andrea Asperti Grzegorz Bancerek Andrzej Trybulec Organization MKM 2004 was organized by the Institute of Computer Science, University of Bialystok in co-operation with the Faculty of Computer Science, Bialystok Technical University and the Association of Mizar Users. Program Committee Andrzej Trybulec (Chair) University of Bialystok, Poland Andrew A. Adams University of Reading, UK Andrea Asperti University of Bologna, Italy Bruno Buchberger RISC Linz, Austria Roy McCasland University of Edinburgh, UK James Davenport University of Bath, UK William M.
Author: Colin McLarty
Publisher: Clarendon Press
ISBN: 0191589497
Category :
Languages : en
Pages : 282
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Book Description
The book covers elementary aspects of category theory and topos theory. It has few mathematical prerequisites, and uses categorical methods throughout rather than beginning with set theoretic foundations. It works with key notions such as cartesian closedness, adjunctions, regular categories, and the internal logic of a topos. Full statements and elementary proofs are given for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the construction of Grothendieck toposes over any topos as base. Three chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis. - ;Introduction; PART I: CATEGORIES: Rudimentary structures in a category; Products, equalizers, and their duals; Groups; Sub-objects, pullbacks, and limits; Relations; Cartesian closed categories; Product operators and others; PART II: THE CATEGORY OF CATEGORIES: Functors and categories; Natural transformations; Adjunctions; Slice categories; Mathematical foundations; PART III: TOPOSES: Basics; The internal language; A soundness proof for topos logic; From the internal language to the topos; The fundamental theorem; External semantics; Natural number objects; Categories in a topos; Topologies; PART IV: SOME TOPOSES: Sets; Synthetic differential geometry; The effective topos; Relations in regular categories; Further reading; Bibliography; Index. -
Author: Arne Hessenbruch
Publisher: Routledge
ISBN: 1134262949
Category : History
Languages : en
Pages : 965
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Book Description
The Reader's Guide to the History of Science looks at the literature of science in some 550 entries on individuals (Einstein), institutions and disciplines (Mathematics), general themes (Romantic Science) and central concepts (Paradigm and Fact). The history of science is construed widely to include the history of medicine and technology as is reflected in the range of disciplines from which the international team of 200 contributors are drawn.
Author: Ivor Grattan-Guiness
Publisher: Routledge
ISBN: 1134887485
Category : History
Languages : en
Pages : 857
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Book Description
First published in 2004. This book examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century. Includes 176 articles contributed by authors of 18 nationalities. With a chronological table of main events in the development of mathematics. Has a fully integrated index of people, events and topics; as well as annotated bibliographies of both classic and contemporary sources and provide unique coverage of Ancient and non-Western traditions of mathematics. Presented in Two Volumes.
