Notes on Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Notes on Set Theory write by Yiannis Moschovakis. This book was released on 2013-04-17. Notes on Set Theory available in PDF, EPUB and Kindle. What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.
Notes on Set Theory
Notes on Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Notes on Set Theory write by Yiannis Moschovakis. This book was released on 1994-02-18. Notes on Set Theory available in PDF, EPUB and Kindle. What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.
Notes on Set Theory
Notes on Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Notes on Set Theory write by Yiannis Moschovakis. This book was released on 2005-12-08. Notes on Set Theory available in PDF, EPUB and Kindle. 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 Logic and Set Theory
Notes on Logic and Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Notes on Logic and Set Theory write by P. T. Johnstone. This book was released on 1987-10-08. Notes on Logic and Set Theory available in PDF, EPUB and Kindle. 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.
A Book of Set Theory
A Book of Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Book of Set Theory write by Charles C Pinter. This book was released on 2014-07-23. A Book of Set Theory available in PDF, EPUB and Kindle. "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"--
