Abstract
In a 1981 paper, Duffus and Rival define an order variety as a class of posets that is closed under the formation of products and retracts. They also introduce the notion of an irreducible poset. In the present paper we define nonextendible colored posets and certain minimal nonextendible colored posets that we call zigzags. We characterize via nonextendible colored posets the order varieties generated by a set of posets. If the generating set contains only finite posets our characterization is via zigzags. By using these theorems we give a characterization of finite irreducible posets.
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