Ordered Sets

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Februar 2005



This detailed textbook presents a great deal of material on ordered sets not previously published in the still rather limited textbook literature. It should be suitable as a text for a course on order theory.


Fundamental notions of set theory.
Fundamental notions.
General relations between posets and their chains and antichains.
Linearly ordered sets.
Products of orders.
Universally ordered sets.
Applications of the splitting method.
The dimension of posets.
Well-founded posets, pwo-sets and trees.
On the order structure of power sets.
Comparison of order types.
Comparability graphs.


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)
EAN: 9780387242194
ISBN: 0387242198
Untertitel: 2005. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: Februar 2005
Seitenanzahl: 400 Seiten
Format: gebunden
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