Extension property for partial automorphisms of the $n$-partite and semigeneric tournaments

Abstract: We present a proof of the extension property for partial automorphisms (EPPA) for classes of finite $n$-partite tournaments for $n \in {2,3,\ldots,\omega}$, and for the class of finite semigeneric tournaments. We also prove that the generic $\omega$-partite tournament and the generic semigeneric tournament have ample generics.