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Author : John P. Mayberry
Publisher : Cambridge University Press
Page : 454 pages
File Size : 41,8 Mb
Release : 2000
Category : Mathematics
ISBN : 0521770343
This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 42,5 Mb
Release : 2020-01-23
Category : History
ISBN : 9781108497824
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author : Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal
Publisher : World Scientific
Page : 222 pages
File Size : 46,9 Mb
Release : 2020-04-04
Category : Mathematics
ISBN : 9789811201943
This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text.
Author : Abraham Adolf Fraenkel
Publisher : Unknown
Page : 297 pages
File Size : 42,5 Mb
Release : 1968
Category : Electronic
ISBN : OCLC:803151895
Author : A.A. Fraenkel,Y. Bar-Hillel,A. Levy
Publisher : Elsevier
Page : 415 pages
File Size : 43,9 Mb
Release : 1973-12-01
Category : Computers
ISBN : 9780080887050
Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.
Author : Jose Ferreiros
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 40,7 Mb
Release : 2001-11-01
Category : Mathematics
ISBN : 3764357495
"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 512 pages
File Size : 42,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486139647
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Author : Robert Lee Moore
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 44,5 Mb
Release : 1932-12-31
Category : Mathematics
ISBN : 9780821810132
Author : Herbert B. Enderton
Publisher : Academic Press
Page : 279 pages
File Size : 48,7 Mb
Release : 1977-05-23
Category : Mathematics
ISBN : 9780080570426
This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Author : Ian Stewart,David Orme Tall
Publisher : Oxford University Press, USA
Page : 409 pages
File Size : 41,9 Mb
Release : 2015
Category : Logic, Symbolic and Mathematical
ISBN : 9780198706434
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
Author : Kenneth Kunen
Publisher : Unknown
Page : 251 pages
File Size : 42,6 Mb
Release : 2009
Category : Mathematics
ISBN : 1904987141
Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.
Author : Stefania Centrone,Deborah Kant,Deniz Sarikaya
Publisher : Springer Nature
Page : 511 pages
File Size : 45,9 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9783030156558
This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.
Author : Charles C Pinter
Publisher : Courier Corporation
Page : 259 pages
File Size : 45,7 Mb
Release : 2014-07-23
Category : Mathematics
ISBN : 9780486497082
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Author : Lech Polkowski
Publisher : Springer Science & Business Media
Page : 549 pages
File Size : 52,9 Mb
Release : 2013-06-05
Category : Mathematics
ISBN : 9783790817768
A comprehensive introduction to mathematical structures essential for Rough Set Theory. The book enables the reader to systematically study all topics of rough set theory. After a detailed introduction in Part 1 along with an extensive bibliography of current research papers. Part 2 presents a self-contained study that brings together all the relevant information from respective areas of mathematics and logics. Part 3 provides an overall picture of theoretical developments in rough set theory, covering logical, algebraic, and topological methods. Topics covered include: algebraic theory of approximation spaces, logical and set-theoretical approaches to indiscernibility and functional dependence, topological spaces of rough sets. The final part gives a unique view on mutual relations between fuzzy and rough set theories (rough fuzzy and fuzzy rough sets). Over 300 excercises allow the reader to master the topics considered. The book can be used as a textbook and as a reference work.
Author : F. William Lawvere,Robert Rosebrugh
Publisher : Cambridge University Press
Page : 280 pages
File Size : 54,5 Mb
Release : 2003-01-27
Category : Mathematics
ISBN : 0521010608
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
