Deciding absorption in relational structures
  We prove that for finite, finitely related algebras the concepts of an absorbing subuniverse and a J\'onsson absorbing subuniverse coincide. Consequently, it is decidable whether a given subset is an absorbing subuniverse of the polymorphism algebra of a given relational structure. 
Libor Barto and Jakub Bul\'in
math.RA