Indivisibility and alpha-morphisms (Q1357270)

A relation \(R\) is \(p\)-divisible if for any partition of its basis into \(p+1\) subsets, \(R\) is embedded into the union of \(p\) subsets. This paper proves a generalization of an earlier result of M. Pouzet: any countable \(p\)-divisible relation embeds two copies of itself intersecting in at most \(p-1\) elements. The main tool of the proof is the notion of \(\alpha\)-morphism introduced in the theory of Ehrenfeucht-Fraïssé games.