On the existence of continua of logics between some intermediate predicate logics (Q1975164)

Since V. A. Jankov proved in 1968 that the class of intermediate propositional logics has the cardinality of the continuum, the study has been developed in several subclasses of intermediate propositional logics by Kuznetsov, Wronski and others. Recently the methods to construct a continuum of logics were applied by Suzuki in the first-order case as well. In this paper the author proves, by refining Suzuki's method, the existence of continua of logics in intervals given by some intermediate predicate logics and their extensions by (a weaker version of) the so-called Kuroda's axiom, which gives rise to a solution of some problems proposed by Suzuki.