Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: From well-quasi-ordered sets to better-quasi-ordered sets. | From well-quasi-ordered sets to better-quasi-ordered sets Maurice Pouzet PCS Universite Claude-Bernard Lyonl Domaine de Gerland -bât. Recherche B 50 avenue Tony-Garnier F69365 Lyon cedex 07 France pouzet@ Norbert Sauer y Department of Mathematics and Statistics The University of Calgary Calgary T2N1N4 Alberta Canada nsauer@ Submitted Jul 17 2005 Accepted Oct 18 2006 Published Nov 6 2006 Mathematics Subject Classihcation 06A06 06A07 Abstract We consider conditions which force a well-quasi-ordered poset wqo to be better-quasi-ordered bqo . In particular we obtain that if a poset P is wqo and the set S P of strictly increasing sequences of elements of P is bqo under domination then P is bqo. As a consequence we get the same conclusion if S P is replaced by J P the collection of non-principal ideals of P or by AM P the collection of maximal antichains of P ordered by domination. It then follows that an interval order which is wqo is in fact bqo. Key words poset ideal antichain domination quasi-order interval-order barrier well-quasiordered set better-quasi-ordered set. Supported by Intas. Research done while the author visited the Math. Dept. of U of C in spring 2005 under a joint agreement between the two universities the support provided is gratefully acknowledged. y Supported by NSERC of Canada Grant 691325 THE ELECTRONIC JOURNAL OF COMBINATORICS 13 2006 R101 1 1 Introduction and presentation of the results How to read this paper Section 7 contains a collection of definitions notations and basic facts. The specialist reader should be able to read the paper with only occasional use of Section 7 to check up on some notation. Section 7 provides readers which are not very familiar with the topic of the paper with some background definitions and simple derivations from those definitions. Such readers will have to peruse Section 7 frequently. The paper is organized as follows. Section 2 provides the basics behind the notion of bqo posets .
