The Structure Of K Cs Transitive Cycle Free Partial Orders

Download or read book The Structure of K-CS-Transitive Cycle-Free Partial Orders written by Richard Warren and published by American Mathematical Society(RI). This book was released on 2014-09-11 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text defines the class of cycle-free partial orders (CFPOs) and gives detailed analysis of the CFPOs fulfilling a natural transitivity assumption, called k-connected set transitivity (k-CS-transitivity). Classification in many cases is given. This work generalizes Droste's classification of the countable k-transitive trees (k>1). In a CFPO, the structure can branch downwards as well as upwards and can do so repeatedly (though it never returns to the starting point by a cycle). Mostly it is assumed that k>2 and that all maximal chains are finite. The main classification splits into the sporadic and skeletal cases. The former is complete in all cardinalities. The latter is performed only in the countable case. The classification is considerably more complicated than for trees and skeletal CFPOs exhibit elaborate and rather surprising behaviour.