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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.My notes
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References found in this work
The mathematics of metamathematics.Helena Rasiowa - 1963 - Warszawa,: Państwowe Wydawn. Naukowe. Edited by Roman Sikorski.
Matrix approach in methodology of sentential calculi.Ryszard Wójcicki - 1973 - Studia Logica 32 (1):7 - 39.
The lattice of strengthenings of a strongly finite consequence operation.Wiesław Dziobiak - 1981 - Studia Logica 40 (2):177 - 193.
Constructing denumerable matrices strongly adequate for pre-finite logics.Ewa Graczyńska & Andrzej Wroński - 1974 - Studia Logica 33 (4):417 - 423.
The degrees of maximality of the intuitionistic propositional logic and of some of its fragments.Wiesław Dziobiak - 1981 - Studia Logica 40 (2):195 - 198.
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