 What is the conclusion of these results? As you know, a logic is like a balance scale: you have expressive power in one pan and computability power in the other. In case you wanted to retain logical properties, you had to change the semantics and lose some expressive power, you cannot have both at a maximum, they are “optimal impossible”. One can express the same idea in a more technical way by resorting to Lindström’s results (Lindström 1969) mentioned in  section 2.3.