Highly set-transitive group action

Definition
A group action on a set is termed highly set-transitive or highly homogeneous if it is $$k$$-set-transitive (in the sense of a multiply set-transitive group action) for every positive integer $$k$$.

Stronger properties

 * Weaker than::Highly transitive group action

Weaker properties

 * Stronger than::Multiply set-transitive group action
 * Stronger than::Transitive group action