Ordered Sets

• Main Author: Harzheim, Egbert (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Springer US, 2005.
• Series: Advances in Mathematics ; 7
• Subjects: Mathematics.; Algebra.; Ordered algebraic structures.; Order, Lattices, Ordered Algebraic Structures.

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....

Table of 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.