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Terminology about trees

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10 1 $begingroup$ In set theory, a tree is usually defined as a partial order such that the set of elements below any given one is well-ordered. I am interested in the class of partial orders $P$ such that for every $p in P$ , the set of $q leq p$ is just linearly ordered. Does this have a name? set-theory terminology posets trees share | cite | improve this question edited Jan 18 at 15:32 Monroe Eskew asked Jan 18 at 12:42 Monroe Eskew Monroe Eskew 7,650...