Ifxyandyx, we writexyand sayxandyareequivalent. We call a set with a preorder aposet.

Contrary to the definition we’ve chosen, the term poset frequently is used to meanpartiallyordered set, rather than preordered set. In category theory terminology, therequirement thatxyimpliesxyis known asskeletality. We thus call partiallyordered setsskeletal posets