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Author: Abraham Adolf Fraenkel
Publisher:
ISBN: 9780720422009
Category : Set theory
Languages : en
Pages : 0
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Book Description
Author: Abraham Adolf Fraenkel
Publisher:
ISBN: 9780720422009
Category : Set theory
Languages : en
Pages : 0
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Book Description
Author: A.A. Fraenkel
Publisher: Elsevier
ISBN: 0080887058
Category : Computers
Languages : en
Pages : 415
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Book Description
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: Robert Lee Moore
Publisher: American Mathematical Soc.
ISBN: 0821810138
Category : Mathematics
Languages : en
Pages : 419
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Book Description
Author: Luca Incurvati
Publisher: Cambridge University Press
ISBN: 1108497829
Category : History
Languages : en
Pages : 255
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Book Description
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author: Douglas Cenzer
Publisher: World Scientific
ISBN: 9811201943
Category : Mathematics
Languages : en
Pages : 222
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Book Description
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: Winfried Just
Publisher: American Mathematical Soc.
ISBN: 0821802666
Category : Mathematics
Languages : en
Pages : 210
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Book Description
This book is an introduction to set theory for beginning graduate students who want to get a sound grounding in those aspects of set theory used extensively throughout other areas of mathematics. Topics covered include formal languages and models, the power and limitation of the Axiomatic Method, the Axiom of Choice, including the fascinating Banach-Tarski Paradox, applications of Zorn's Lemma, ordinal arithmetic, including transfinite induction, and cardinal arithmetic. The style of writing, more a dialogue with the reader than that of the Master indoctrinating the pupil, makes this also very suitable for self-study.
Author: John P. Mayberry
Publisher: Cambridge University Press
ISBN: 9780521770347
Category : Mathematics
Languages : en
Pages : 454
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Book Description
This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Author: Azriel Levy
Publisher: Courier Corporation
ISBN: 0486150739
Category : Mathematics
Languages : en
Pages : 418
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Book Description
Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.
Author: Penelope Maddy
Publisher: Oxford University Press
ISBN: 0199596182
Category : Mathematics
Languages : en
Pages : 161
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Book Description
Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.
Author: Stefania Centrone
Publisher: Springer Nature
ISBN: 3030156559
Category : Mathematics
Languages : en
Pages : 511
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Book Description
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.
