Submission date: 27 April 2021

Abstract:

We show that the existence of a universal structure, for an approximable class C of countable structures, implies the existence of a generic structure for C. We also show that the converse is not true. As a consequence, we provide several new examples of weak Fraït;ssé classes of finite graphs. Finally, we show that the class of all countable C_4-free graphs does not contain a generic structure, strengthening a result of A. Hajnal and J. Pach.

Mathematics Subject Classification: 05C75, 05C38, 03C52

Keywords and phrases:

Full text arXiv 2104.13222: pdf, ps.