Labels: Set Theory. Unknown February 5, at PM. Newer Post Older Post Home. Subscribe to: Post Comments Atom. 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. Author : Paul Halmos Publisher: ISBN: Category: Page: View: Read Now » This book "Naive Set Theory" uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study.
The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics. Author : D. Applications of the axiom of choice are also discussed, along with infinite games and the axiom of determinateness.
The equality of sets, subsets, and ordered pairs are considered, together with equivalence relations and real numbers. The next chapter is devoted to axiomatic set theory and discusses the axiom of regularity, induction and recursion, and ordinal and cardinal numbers. In the final chapter, applications of set theory are reviewed, paying particular attention to filters, Boolean algebra, and inductive definitions together with trees and the Borel hierarchy.
Suitable for advanced undergraduates and graduate students in mathematics, it employs the language and notation of informal mathematics. There are very few displayed theorems; most of the facts are stated in simple terms, followed by a sketch of the proof. Only a few exercises are designated as such since the book itself is an ongoing series of exercises with hints.
The treatment covers the basic concepts of set theory, cardinal numbers, transfinite methods, and a good deal more in 25 brief chapters. It is aimed at 'the beginning student of advanced mathematics' … who wants to understand the set-theoretic underpinnings of the mathematics he already knows or will learn soon.
It is also useful to the professional mathematician who knew these underpinnings at one time but has now forgotten exactly how they go.
Author : K. 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. 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?
Author : J. Three examples of such models are investigated in Chapters VI, VII, and VIII; the most important of these, the class of constructible sets, leads to G6del's result that the axiom of choice and the continuum hypothesis are consistent with the rest of set theory [1]I. The text thus constitutes an introduction to the results of P. Cohen concerning the independence of these axioms [2], and to many other relative consistency proofs obtained later by Cohen's methods.
Chapters I and II introduce the axioms of set theory, and develop such parts of the theory as are indispensable for every relative consistency proof; the method of recursive definition on the ordinals being an import ant case in point.
Although, more or less deliberately, no proofs have been omitted, the development here will be found to require of the reader a certain facility in naive set theory and in the axiomatic method, such e as should be achieved, for example, in first year graduate work 2 cycle de mathernatiques. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure.
A final chapter presents an alternative conception of set theory useful in computer science.
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