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Given a collection S of sets, a set S∈S is said to be strongly maximal in S if |T∖S|≤|S∖T| 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”...
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