caa a22 4500 386307512 CHVBK 20180307111534.0 cr unu---uuuuu 161130e198806 xx s 000 0 eng 10.1017/S1446788700032110 doi S1446788700032110 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700032110 Williams N. H. Department of Mathematics University of Queensland St. Lucia, Queensland 4067, Australia An order property for families of sets [Elektronische Daten] [N. H. Williams] We develop the idea of a θ-ordering (where θ is an infinite cardinal) for a family of infinite sets. A θ-ordering of the family A is a well ordering of A which decomposes A into a union of pairwise disjoint intervals in a special way, which facilitates certain transfinite constructions. We show that several standard combinatorial properties, for instance that of the family A having a θ-transversal, are simple consequences of A possessing a θ-ordering. Most of the paper is devoted to showing that under suitable restrictions, an almost disjoint family will have a θ-ordering. The restrictions involve either intersection conditions on A (the intersection of every λ-size subfamily of A has size at most κ) or a chain condition on A. Copyright © Australian Mathematical Society 1988 03 E 05 nationallicence 04 A 20 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 44/3(1988-06), 294-310 1446-7887 44:3<294 1988 44 JAZ https://doi.org/10.1017/S1446788700032110 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700032110 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Williams N. H. Department of Mathematics University of Queensland St. Lucia, Queensland 4067, Australia NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 44/3(1988-06), 294-310 1446-7887 44:3<294 1988 44 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge