Advances in Mathematics

Ordered Sets

Authors: Harzheim, Egbert

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About this Textbook

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 naïve 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.

Reviews

From the reviews:

"The exposition of material in Ordered Sets is generally quite clear. … The list of symbols is useful. … the book contains an unusual mix of topics that reflects both the author’s varied interests and developments in the theory of infinite ordered sets, particularly concerning universal orders, the splitting method, and aspects of well-quasi ordering. It will be of greatest interest to readers who want a selective treatment of such topics." (Dwight Duffus, SIAM Review, Vol. 48 (1), 2006)

"The textbook literature on ordered sets is rather limited. So this book fills a gap. It is intended for mathematics students and for mathematicians who are interests in ordered sets." (Martin Weese, Zentralblatt MATH, Vol. 1072, 2005)

"This book is a comprehensive introduction to the theory of partially ordered sets. It is a fine reference for the practicing mathematician, and an excellent text for a graduate course. Chains, antichains, linearly ordered sets, well-ordered sets, well-founded sets, trees, embedding, cofinality, products, topology, order types, universal sets, dimension, ordered subsets of power sets, comparability graphs, a little partition calculus … it’s pretty much all here, clearly explained and well developed." (Judith Roitman, Mathematical Reviews, Issue 2006 e)


Table of contents (1 chapters)

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-0-387-24222-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.00
price for USA
  • ISBN 978-0-387-24219-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $199.00
price for USA
  • ISBN 978-1-4419-3704-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Ordered Sets
Authors
Series Title
Advances in Mathematics
Series Volume
7
Copyright
2005
Publisher
Springer US
Copyright Holder
Springer-Verlag US
eBook ISBN
978-0-387-24222-4
DOI
10.1007/b104891
Hardcover ISBN
978-0-387-24219-4
Softcover ISBN
978-1-4419-3704-9
Edition Number
1
Number of Pages
XII, 386
Topics