ABSTRACT
It should further be noticed that the calculus MK cannot be subjected to restrictions on the size of the succedent N in its sequents M = > N - say to contain 27 members only. This is illustrated b the following exam ple, due to ULRICH MAYER. The endsequent of the M K -derivation
A =4 -ixA-ny, x ,y
cannot be the conclusion from M K -derivable prem isses w ith succedents of only 2 members. Because the only possible rules from which to obtain it would be (Ia) or (Iv), and in the first case the prem isses would have to be the sequents
a = > x or a = > (-ixA-iy)v(-ixAy)
and in the second case
a = $ x , “ixA~iy or a = $ x, “ixAy
all of which are underivable. In the same way, the M K -derivable sequent
cannot be the conclusion from M K -derivable prem isses w ith succedents of only 27 members.
