Foundations of Point Set Theory
Author | : Robert Lee Moore |
Publisher | : American Mathematical Soc. |
Total Pages | : 434 |
Release | : 1932-12-31 |
Genre | : Mathematics |
ISBN | : 0821810138 |
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Author | : Robert Lee Moore |
Publisher | : American Mathematical Soc. |
Total Pages | : 434 |
Release | : 1932-12-31 |
Genre | : Mathematics |
ISBN | : 0821810138 |
Author | : Robert Lee Moore |
Publisher | : American Mathematical Soc. |
Total Pages | : 434 |
Release | : 1932 |
Genre | : Set theory |
ISBN | : 0821874500 |
Author | : Luca Incurvati |
Publisher | : Cambridge University Press |
Total Pages | : 255 |
Release | : 2020-01-23 |
Genre | : History |
ISBN | : 1108497829 |
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author | : Abhijit Dasgupta |
Publisher | : Springer Science & Business Media |
Total Pages | : 434 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 1461488540 |
What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.
Author | : Andre L. Yandl |
Publisher | : Courier Dover Publications |
Total Pages | : 260 |
Release | : 2016-04-10 |
Genre | : Mathematics |
ISBN | : 0486811018 |
In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses. Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations. "This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." — Mathematical Association of America
Author | : Sean Morris |
Publisher | : Cambridge University Press |
Total Pages | : 221 |
Release | : 2018-12-13 |
Genre | : History |
ISBN | : 110715250X |
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Author | : Tim Maudlin |
Publisher | : |
Total Pages | : 374 |
Release | : 2014-02 |
Genre | : Mathematics |
ISBN | : 0198701306 |
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Author | : Douglas Cenzer |
Publisher | : World Scientific |
Total Pages | : 222 |
Release | : 2020-04-04 |
Genre | : Mathematics |
ISBN | : 9811201943 |
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 | : Penelope Maddy |
Publisher | : Oxford University Press |
Total Pages | : 161 |
Release | : 2011-01-27 |
Genre | : Mathematics |
ISBN | : 0199596182 |
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 | : A.A. Fraenkel |
Publisher | : Elsevier |
Total Pages | : 415 |
Release | : 1973-12-01 |
Genre | : Computers |
ISBN | : 0080887058 |
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.