A Note on the Number of Subnormal Modal Logics

Patryk Michalczenia

doi:10.18778/0138-0680.2026.19

Authors

Patryk Michalczenia University of Wrocław, Department of Logic and Methodology of Sciences, Wrocław, Poland Author https://orcid.org/0000-0002-7908-7801

DOI:

https://doi.org/10.18778/0138-0680.2026.19

Keywords:

subnormal, modal, continuum, cardinality

Abstract

In the article we discuss the notion of a subnormal modal logic and, in particular, the notion of an intermediate subnormal modal logic. The goal of the article is to determine the cardinality of the set of all intermediate subnormal modal logics. Thus we define a set of certain formulas, such that each subset of the defined set determines a different intermediate subnormal modal logic. As we demonstrate, since the set in question is countable, the set of all intermediate subnormal modal logics has cardinality of the continuum.

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