A study of intermediate propositional logics on the third slice

Abstract

The intermediate logics have been classified into slices (cf. Hosoi [1]), but the detailed structure of slices has been studied only for the first two slices (cf. Hosoi and Ono [2]). In order to study the structure of slices, we give a method of a finer classification of slices & n (n ≥ 3). Here we treat only the third slice as an example, but the method can be extended to other slices in an obvious way. It is proved that each subslice contains continuum of logics. A characterization of logics in each subslice is given in terms of the form of models.