[FOM] lattices of logics

[Adam Kolany]

Hi,

it is known that the fixpoints (=theories) of consequence operators for
overintuitionistic logics form Heyting algebras.
One has been proven
[
W. Dzik, On the content of lattices of logics. Part I,
Reports on Mathematical Logic, No 13, (1981), pp. 17–28.
W. Dzik, On the content of lattices of logics. Part II,
Reports on Mathematical Logic, No 14, (1982), pp. 29–47.
]
that the content of (all the formulas true in) l_CLC is INT and
that of l_INT is WEM. there are also some more interesting results.
However I do not know anything of the content of the lattice of ALL
superintuitionistic logics (which also is a Heyting algebra).

Can someone tell me anything on this topic?

Thanks,

Adam Kolany,