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Author: Peter Komjath
Publisher: Springer Science & Business Media
ISBN: 038730293X
Category : Mathematics
Languages : en
Pages : 492
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Book Description
This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.
Author: Peter Komjath
Publisher: Springer Science & Business Media
ISBN: 038730293X
Category : Mathematics
Languages : en
Pages : 492
Get Book
Book Description
This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.
Author: Peter Komjath
Publisher: Springer Science & Business Media
ISBN: 0387362193
Category : Mathematics
Languages : en
Pages : 516
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Book Description
This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.
Author: D.C. Goldrei
Publisher: Routledge
ISBN: 1351460617
Category : Mathematics
Languages : en
Pages : 296
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Book Description
Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.
Author: Abhijit Dasgupta
Publisher: Springer Science & Business Media
ISBN: 1461488540
Category : Mathematics
Languages : en
Pages : 444
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Book Description
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: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486497089
Category : Mathematics
Languages : en
Pages : 259
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Book Description
"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"--
Author: Raymond M. Smullyan
Publisher:
ISBN: 9780486474847
Category : Continuum hypothesis
Languages : en
Pages : 0
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Book Description
A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.
Author: Yiannis N. Moschovakis
Publisher: American Mathematical Soc.
ISBN: 0821848135
Category : Mathematics
Languages : en
Pages : 521
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Book Description
Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and so can be expected to have special properties not enjoyed by arbitrary pointsets. This subject was started by the French analysts at the turn of the 20th century, most prominently Lebesgue, and, initially, was concerned primarily with establishing regularity properties of Borel and Lebesgue measurable functions, and analytic, coanalytic, and projective sets. Its rapid development came to a halt in the late 1930s, primarily because it bumped against problems which were independent of classical axiomatic set theory. The field became very active again in the 1960s, with the introduction of strong set-theoretic hypotheses and methods from logic (especially recursion theory), which revolutionized it. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern ``effective'' theory and the consequences of strong (especially determinacy) hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results (established since the 1980s) relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics. The book includes all the necessary background from (advanced) set theory, logic and recursion theory.
Author: Alexander Kechris
Publisher: Springer Science & Business Media
ISBN: 1461241901
Category : Mathematics
Languages : en
Pages : 419
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Book Description
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.
Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486139646
Category : Mathematics
Languages : en
Pages : 512
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Book Description
Explores 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.
Author: Wolf Schwarz
Publisher: Springer Science & Business Media
ISBN: 0387735127
Category : Mathematics
Languages : en
Pages : 124
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Book Description
This book is based on the view that cognitive skills are best acquired by solving challenging, non-standard probability problems. Many puzzles and problems presented here are either new within a problem solving context (although as topics in fundamental research they are long known) or are variations of classical problems which follow directly from elementary concepts. A small number of particularly instructive problems is taken from previous sources which in this case are generally given. This book will be a handy resource for professors looking for problems to assign, for undergraduate math students, and for a more general audience of amateur scientists.
