Cardinalities of proper ideals in some lattices of strengthenings of the intuitionistic propositional logic

Studia Logica 42 (2-3):173 - 177 (1983)
Abstract
We prove that each proper ideal in the lattice of axiomatic, resp. standard strengthenings of the intuitionistic propositional logic is of cardinality 20. But, each proper ideal in the lattice of structural strengthenings of the intuitionistic propositional logic is of cardinality 220. As a corollary we have that each of these three lattices has no atoms.
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