Given a collection S of sets, a set S∈S is said to be strongly maximal in S if TS|≤|ST| for every T∈S. In Aharoni (1991) [3] it was shown that a poset with no infinite chain must contain a strongly maximal antichain. In this paper we show that for countable posets it suffices to demand that the poset does not contain a copy of posets of two types: a binary tree (going up or down) or a "pyramid". The latter is a poset consisting of disjoint antichains ~(Ai)s,i=1,2,..., such that |~(Ai)|=i and x展开▼
机译：给定集合的集合S，如果T S |≤| S T |，则集合S∈S在S中被认为是极大的。对于每个T∈S。在Aharoni（1991）[3]中，没有无限链的波塞必须包含一个最大的反链。在本文中，我们表明，对于可数的姿势，仅要求姿势不包含两种类型的姿势副本就足够了：二叉树（向上或向下）或“金字塔”。后者是由不相交的反链〜（Ai）s，i = 1,2，...组成的坐姿，使得|〜（Ai）| = i和x 展开▼
