notes on set theory undergraduate texts in mathematics

Download Book Notes On Set Theory Undergraduate Texts In Mathematics in PDF format. You can Read Online Notes On Set Theory Undergraduate Texts In Mathematics here in PDF, EPUB, Mobi or Docx formats.

Notes On Set Theory

Author : Yiannis N. Moschovakis
ISBN : 3540941800
Genre : Axiomatische Mengenlehre
File Size : 31. 6 MB
Format : PDF, ePub
Download : 117
Read : 399

Get This Book


The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise" simply means "to define it in set theory." This book gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and rearranged and reworked the text to improve the presentation.

Notes On Set Theory

Author : Yiannis Moschovakis
ISBN : 038728723X
Genre : Mathematics
File Size : 65. 22 MB
Format : PDF, ePub, Mobi
Download : 399
Read : 966

Get This Book


The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise" simply means "to define it in set theory." This book gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and rearranged and reworked the text to improve the presentation.

Notes On Set Theory

Author : Yiannis N. Moschovakis
ISBN : 9780387941806
Genre : Mathematics
File Size : 51. 67 MB
Format : PDF
Download : 650
Read : 1249

Get This Book


"The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice "to make a notion precise" simply means "to define it in set theory." This book tries to do justice to both aspects of the subject: it gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets (including the basic results that have applications to computer science), but it also attempts to explain precisely how mathematical objects can be faithfully modeled within the universe of sets." "Topics covered include the naive theory of equinumerosity; paradoxes and axioms; modeling mathematical notions by sets; cardinal numbers; natural numbers; fixed points (continuous least-fixed-point theorem); well-ordered sets (transfinite induction and recursion, Hartogs' theorem, comparability of well-ordered sets, least-fixed-point theorem); the Axiom of Choice and its consequences; Baire space (Cantor-Bendixson theorem, analytic pointsets, perfect set theorem); Replacement and other axioms; ordinal numbers. There is an Appendix on the real numbers and another on natural models, including the antifounded universe." "The book is aimed at advanced undergraduate or beginning graduate mathematics students and at mathematically minded graduate students of computer science and philosophy."--BOOK JACKET.

Notes On Logic And Set Theory

Author : P. T. Johnstone
ISBN : 0521336929
Genre : Mathematics
File Size : 49. 69 MB
Format : PDF, ePub
Download : 721
Read : 470

Get This Book


A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics.

Naive Set Theory

Author : P. R. Halmos
ISBN : 9781475716450
Genre : Mathematics
File Size : 42. 74 MB
Format : PDF, Mobi
Download : 458
Read : 1057

Get This Book


Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.

Set Theory For The Working Mathematician

Author : Krzysztof Ciesielski
ISBN : 0521594650
Genre : Mathematics
File Size : 38. 4 MB
Format : PDF, Kindle
Download : 296
Read : 660

Get This Book


Presents those methods of modern set theory most applicable to other areas of pure mathematics.

The Real Numbers

Author : John Stillwell
ISBN : 9783319015774
Genre : Mathematics
File Size : 62. 14 MB
Format : PDF, ePub, Docs
Download : 184
Read : 314

Get This Book


While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.

Set Theory An Introduction

Author : Robert L. Vaught
ISBN : 0817642560
Genre : Mathematics
File Size : 90. 52 MB
Format : PDF, Kindle
Download : 725
Read : 601

Get This Book


An excellent undergraduate text on set theory that could be used in courses taught in mathematics and philosophy departments. The intuitive development in the first chapters also makes the book suitable for self study.

Set Theory Logic And Their Limitations

Author : Moshe Machover
ISBN : 0521479983
Genre : Mathematics
File Size : 22. 95 MB
Format : PDF, ePub
Download : 569
Read : 405

Get This Book


Rigorous coverage of logic and set theory for students of mathematics and philosophy.

An Outline Of Set Theory

Author : James M. Henle
ISBN : 9780486453378
Genre : Mathematics
File Size : 63. 6 MB
Format : PDF, ePub, Mobi
Download : 466
Read : 1289

Get This Book


An innovative problem-oriented introduction to set theory, this volume is intended for undergraduate courses in which students work in groups on projects and present their solutions to the class. The three-part treatment consists of problems, hints for their solutions, and complete answers. 1986 edition.

Top Download:

Best Books