Download or read book Set Theory and Hierarchy Theory written by W. Marek and published by Springer. This book was released on 2006-11-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Hierarchy of Formulas in Set Theory written by Azriel Levy and published by American Mathematical Soc.. This book was released on 1965 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Notes on Set Theory written by Yiannis Moschovakis and published by Springer Science & Business Media. This book was released on 2006-06-15 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Set Theory and Hierarchy Theory V written by A. Lachlan and published by Springer. This book was released on 2006-11-15 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Set Theory and Hierarchy Theory V written by Alistair Lachlan and published by . This book was released on 2014-01-15 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Set Theory and Hierarchy Theory written by W. Marek and published by . This book was released on 2014-01-15 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Set Theory written by John P. Burgess and published by Cambridge University Press. This book was released on 2022-03-10 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.

Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--

Download or read book Set Theory written by Andras Hajnal and published by Cambridge University Press. This book was released on 1999-11-11 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appendix to the first part gives a more formal foundation to axiomatic set theory, supplementing the intuitive introduction given in the first part. The final part gives an introduction to modern tools of combinatorial set theory. This part contains enough material for a graduate course of one or two semesters. The subjects discussed include stationary sets, delta systems, partition relations, set mappings, measurable and real-valued measurable cardinals. Two sections give an introduction to modern results on exponentiation of singular cardinals, and certain deeper aspects of the topics are developed in advanced problems.

Download or read book Essential Concepts of Set Theory written by Robert S. Y. Wong and published by 香港教育圖書公司. This book was released on 2016-07-01 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: For thousands of years, it is generally believed that mathematics begins with the natural numbers and counting. But there is something more fundamental than counting. It is the grouping of things. If a child is shown a picture of a farm with sheep and cows here and there and asked to count the number of sheep, the child would first put the sheep in a group mentally and then count the number of sheep in the group. Without grouping, counting cannot happen. Therefore, mathematics begins with the grouping of objects, which is the object of study of set theory. In this book, we explore the fundamental concepts of sets and related topics: propositional logic, methods of proof, relations and functions. Unlike the technical approach adopted in most books, we use many everyday examples to show that these concepts can be found everywhere in our daily life. The book also has plenty of exercises and solutions to all exercises are provided.

Download or read book Set Theory and Hierarchy Theory V written by and published by . This book was released on 1977 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Set Theory written by Abhijit Dasgupta and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Handbook of Set Theory written by Matthew Foreman and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 2200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.

Download or read book Fundamentals of Contemporary Set Theory written by K. J. Devlin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to provide an account of those parts of contemporary set theory which are of direct relevance to other areas of pure mathematics. The intended reader is either an advanced level undergraduate, or a beginning graduate student in mathematics, or else an accomplished mathematician who desires or needs a familiarity with modern set theory. The book is written in a fairly easy going style, with a minimum of formalism (a format characteristic of contemporary set theory) • In Chapter I the basic principles of set theory are developed in a "naive" tl manner. Here the notions of "set I II union " , "intersection", "power set" I "relation" I "function" etc. are defined and discussed. One assumption in writing this chapter has been that whereas the reader may have met all of these concepts before, and be familiar with their usage, he may not have considered the various notions as forming part of the continuous development of a pure subject (namely set theory) • Consequently, our development is at the same time rigorous and fast. Chapter II develops the theory of sets proper. Starting with the naive set theory of Chapter I, we begin by asking the question "What is a set?" Attempts to give a rLgorous answer lead naturally to the axioms of set theory introduced by Zermelo and Fraenkel, which is the system taken as basic in this book.

Download or read book Introduction to Modern Set Theory written by Judith Roitman and published by John Wiley & Sons. This book was released on 1990-01-16 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.

Download or read book A Set Theory Workbook written by Iain Adamson and published by Springer Science & Business Media. This book was released on 1997-12-18 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a companion to A general topology workbook published by Birkhiiuser last year. In an ideal world the order of publication would have been reversed, for the notation and some of the results of the present book are used in the topology book and on the other hand (the reader may be assured) no topology is used here. Both books share the word Workbook in their titles. They are based on the principle that for at least some branches of mathematics a good way for a student to learn is to be presented with a clear statement of the definitions of the terms with which the subject is concerned and then to be faced with a collection of problems involving the terms just defined. In adopting this approach with my Dundee students of set theory and general topology I found it best not to differentiate too precisely between simple illustrative examples, easy exercises and results which in conventional textbooks would be labelled as Theorems.

Download or read book Elements of Set Theory written by Herbert B. Enderton and published by Gulf Professional Publishing. This book was released on 1977-04-28 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.