TY - BOOK
AU - Harzheim,Egbert
ED - SpringerLink (Online service)
TI - Ordered Sets
T2 - Advances in Mathematics
SN - 9780387242224
AV - QA172-172.4
U1 - 511.33 23
PY - 2005///
CY - Boston, MA
PB - Springer US
KW - Mathematics
KW - Algebra
KW - Ordered algebraic structures
KW - Order, Lattices, Ordered Algebraic Structures
N1 - 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
N2 - 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
UR - http://dx.doi.org/10.1007/b104891
ER -