Posets, homomorphisms and homogeneity Abstract

Jarik Neˇsetˇril suggested to the first author the investigation of notions of homogeneity for relational structures, where “isomorphism ” is replaced by “homomorphism” in the definition. Here we look in detail at what happens for posets. For the strict order, all five generalisations of homogeneity coincide, and we give a characterisation of the countable structures that arise. For the non-strict order, there is an additional class. The “generic poset ” plays an important role in the investigation. Key words: Poset, homomorphism, homogeneous, relational structure