Ordered Sets Hardcover - 2005 - 2005th Edition

Name: Ordered Sets
Price: 155.73 GBP
Availability: InStock
Author: Egbert Harzheim
ISBN: 9780387242194

by Egbert Harzheim

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From the publisher

This book is written particularly for mathematics students and, of course, for mathematicians interested in set theory. Only some fun- mental parts of naive set theory are presupposed, - not more than is treated in a textbook on set theory, even if this restricts us only to the most basic facts of this field. We have summarized all of this in Chapter 0 without longer discusssions and explanations, because there are s- eral textbooks which can be consulted by the reader, e.g. HrbacekIJech [88], KneeboneIRotman [99], ShenIVereshchagin [159]. Besides this only elementary facts of analysis are used. The theory of ordered sets can be divided into two parts, depending on whether the sets under consideration are finite or infinite. The first part is grounded mainly in combinatorics and graph theory and does not make essential use of set-theorical concepts, whereas the second part presupposes a knowledge of the fundamental notions of set theory, in particular of the system of ordinal and cardinal numbers. In this book we mainly deal with general infinite ordered sets. In this field the textbook literature is still very small. Therefore this book supplements the existing literature.

From the rear cover

The textbook literature on ordered sets is still rather limited. A lot of material is presented in this book that appears now for the first time in a textbook.

Order theory works with combinatorial and set-theoretical methods, depending on whether the sets under consideration are finite or infinite. In this book the set-theoretical parts prevail. The book treats in detail lexicographic products and their connections with universally ordered sets, and further it gives thorough investigations on the structure of power sets. Other topics dealt with include dimension theory of ordered sets, well-quasi-ordered sets, trees, combinatorial set theory for ordered sets, comparison of order types, and comparibility graphs.

Audience

This book is intended for mathematics students and for mathemeticians who are interested in set theory. Only some fundamental parts of na�ve set theory are presupposed. Since all proofs are worked out in great detail, the book should be suitable as a text for a course on order theory.