Consider the lattice of consistent superintuitionistic logics, also known as intermediate logics. Smetanich's logic is the logic obtained from intuitionistic logic by adding the axiom $((\neg q \rightarrow p) \rightarrow (((p \rightarrow q) \rightarrow p) \rightarrow p))$. I have read it is the unique coatom in the lattice of intermediate logics. But that is a weaker condition than being second from the top. More precisely, if you remove classical logic from the lattice of intermediate logics, would Smetanich's logic be the new top element?
Asked
Active
Viewed 63 times
