02682nam a22004215i 4500001001800000003000900018005001700027007001500044008004100059020001800100024002500118050001600143050001200159072001600171072002300187082001500210100003100225245006300256264003800319300003400357336002600391337002600417338003600443347002400479490003300503505040800536520102300944650001701967650001301984650003401997650001702031650005102048710003402099773002002133776003602153830003302189856003802222978-0-387-24222-4DE-He21320180115171349.0cr nn 008mamaa100301s2005 xxu| s |||| 0|eng d a97803872422247 a10.1007/b1048912doi 4aQA172-172.4 4aQA171.5 7aPBF2bicssc 7aMAT0020102bisacsh04a511.332231 aHarzheim, Egbert.eauthor.10aOrdered Setsh[electronic resource] /cby Egbert Harzheim. 1aBoston, MA :bSpringer US,c2005. aXII, 386 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aAdvances in Mathematics ;v70 aFundamental 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. aThe 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 naìˆve 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. 0aMathematics. 0aAlgebra. 0aOrdered algebraic structures.14aMathematics.24aOrder, Lattices, Ordered Algebraic Structures.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387242194 0aAdvances in Mathematics ;v740uhttp://dx.doi.org/10.1007/b104891