Martin Lof random and PA complete sets
A set A is Martin LL of random ii the class fAg does not have 0 1 measure 0. A set A is PA complete if one can compute relative to A a consistent and complete extension of Peano Arithmetic. It is shown that every Martin LL of random set either permits to solve the halting problem K or is not PA complete. This result implies a negative answer to the question of Ambos Spies and Ku cera whether there is a Martin LL of random set not above K which is also PA complete.