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Author: Juliette Kennedy Publisher: Cambridge University Press ISBN: 9781107008045 Category : Mathematics Languages : en Pages : 242
Book Description
This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum's theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972-1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse view; Anne Troelstra's history of intuitionism through 1991; and Aki Kanamori's history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory, and is ideal for researchers and graduate students in mathematical logic and philosophy of mathematics.
Author: Juliette Kennedy Publisher: Cambridge University Press ISBN: 9781107008045 Category : Mathematics Languages : en Pages : 242
Book Description
This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum's theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972-1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse view; Anne Troelstra's history of intuitionism through 1991; and Aki Kanamori's history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory, and is ideal for researchers and graduate students in mathematical logic and philosophy of mathematics.
Author: Norman T. Hamilton Publisher: Courier Dover Publications ISBN: 0486830470 Category : Mathematics Languages : en Pages : 289
Book Description
This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.
Author: Douglas Cenzer Publisher: World Scientific ISBN: 9811201943 Category : Mathematics Languages : en Pages : 222
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: A.A. Fraenkel Publisher: Elsevier ISBN: 0080887058 Category : Computers Languages : en Pages : 415
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: F. William Lawvere Publisher: Cambridge University Press ISBN: 9780521010603 Category : Mathematics Languages : en Pages : 280
Book Description
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
Author: Robert Roth Stoll Publisher: Courier Corporation ISBN: 0486638294 Category : Mathematics Languages : en Pages : 516
Book Description
"The best introductory text we have seen." — Cosmos. Lucidly and gradually explains 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. Its clarity makes this book excellent for self-study.
Author: Winfried Just Publisher: American Mathematical Soc. ISBN: 0821802666 Category : Mathematics Languages : en Pages : 230
Book Description
This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.
Author: M.A. Armstrong Publisher: Springer Science & Business Media ISBN: 1475717938 Category : Mathematics Languages : en Pages : 260
Book Description
In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties help students gain a thorough understanding of the subject.
Author: Joseph Breuer Publisher: Courier Corporation ISBN: 0486154874 Category : Mathematics Languages : en Pages : 130
Book Description
This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
Author: Juliette Kennedy
Author: Juliette Kennedy
Author: Norman T. Hamilton
Author: Douglas Cenzer
Author: A.A. Fraenkel
Author: F. William Lawvere
Author: Robert Roth Stoll
Author: Juliette Kennedy
Author: Winfried Just
Author: M.A. Armstrong
Author: Joseph Breuer