Foundations of Point Set Theory
Author : Robert Lee Moore
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 16,98 MB
Release : 1932-12-31
Category : Mathematics
ISBN : 0821810138
Author : Robert Lee Moore
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 16,98 MB
Release : 1932-12-31
Category : Mathematics
ISBN : 0821810138
Author : Robert Lee Moore
Publisher :
Page : 430 pages
File Size : 20,22 MB
Release : 2012-07-01
Category :
ISBN : 9781258437503
Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 32,52 MB
Release : 2020-01-23
Category : 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
Page : 434 pages
File Size : 37,19 MB
Release : 2013-12-11
Category : 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 : Sean Morris
Publisher : Cambridge University Press
Page : 221 pages
File Size : 35,3 MB
Release : 2018-12-13
Category : History
ISBN : 110715250X
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Author : Jose Ferreiros
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 36,93 MB
Release : 2001-11-01
Category : Mathematics
ISBN : 9783764357498
"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 : Penelope Maddy
Publisher : Oxford University Press
Page : 161 pages
File Size : 23,24 MB
Release : 2011-01-27
Category : 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 : F. William Lawvere
Publisher : Cambridge University Press
Page : 280 pages
File Size : 10,86 MB
Release : 2003-01-27
Category : Mathematics
ISBN : 9780521010603
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
Author : Tim Maudlin
Publisher :
Page : 374 pages
File Size : 18,21 MB
Release : 2014-02
Category : 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 : Charles C Pinter
Publisher : Courier Corporation
Page : 259 pages
File Size : 34,34 MB
Release : 2014-07-23
Category : Mathematics
ISBN : 0486497089
"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"--