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

  • I. Propositional Calculi, Their Methodology And Philosophical Applications
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Abstract

We prove that each proper ideal in the lattice of axiomatic, resp. standard strengthenings of the intuitionistic propositional logic is of cardinality 2ℵ0. But, each proper ideal in the lattice of structural strengthenings of the intuitionistic propositional logic is of cardinality 22ℵ0. As a corollary we have that each of these three lattices has no atoms.

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Authors and Affiliations

  1. Section of Logic Institute of Philosophy and Sociology, Polish Academy of Sciences, Poland

    Wiesław Dziobiak

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  1. Wiesław Dziobiak
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Dziobiak, W. Cardinalities of proper ideals in some lattices of strengthenings of the intuitionistic propositional logic. Stud Logica 42, 173–177 (1983). https://doi.org/10.1007/BF01063837

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  • DOI: https://doi.org/10.1007/BF01063837

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