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Ordered Sets

By: Harzheim, Egbert [author.].
Contributor(s): SpringerLink (Online service)0.
Material type: materialTypeLabelBookSeries: Advances in Mathematics: 74Publisher: Boston, MA : Springer US, 2005.Description: XII, 386 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780387242224.Subject(s): Mathematics | Algebra | Ordered algebraic structures.1 | Mathematics.2 | Order, Lattices, Ordered Algebraic Structures.2DDC classification: 511.33 Online resources: Click here to access online
Contents:
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.
In: Springer eBooks0Summary: 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.
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Item type Current location Call number Status Date due Barcode Item holds
PK Kelkar Library, IIT Kanpur
Available EBK6229
Total holds: 0

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.

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.

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