Ordered Sets

Egbert Harzheim (auth.)9780387242194, 0-387-24219-8

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.

Table of contents :
Fundamental notions of set theory….Pages 1-9
Fundamental notions….Pages 11-47
General relations between posets and their chains and antichains….Pages 49-70
Linearly ordered sets….Pages 71-83
Products of orders….Pages 85-141
Universally ordered sets….Pages 143-158
Applications of the splitting method….Pages 159-201
The dimension of posets….Pages 203-230
Well-founded posets, pwo-sets and trees….Pages 231-284
On the order structure of power sets….Pages 285-329
Comparison of order types….Pages 331-352
Comparability graphs….Pages 353-368