Egbert Harzheim

Ordered Sets (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer US
• Seitenzahl: 386
• Erscheinungstermin: 25. Juli 2005
• Englisch
• ISBN-13: 9780387242224
• Artikelnr.: 43730216

Autorenporträt

Egbert Harzheim, University of Düsseldorf, Germany

Inhaltsangabe

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.

Rezensionen

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)