  One of Gupta and Belnap's principle open questions is whether there is a complete calculus for these systems: that is, whether, for each definition D, either of the following two sets of sentences is recursively axiomatizable:  {B : ⊨*,D B} and   {B : ⊨#,D B}.  Kremer 1993 proves that the answer is no: he shows that there is a definition D such that each of these sets of sentences is of complexity at least Π12, thereby putting a lower limit on the complexity of S* and S#. (Antonelli 1994a and 2002 shows that this is also an upper limit.) 