Constructing a continuum of predicate extensions of each intermediate propositional logic

Wajsberg and Jankov provided us with methods of constructing a continuum of logics. However, their methods are not suitable for super-intuitionistic and modal predicate logics. The aim of this paper is to present simple ways of modification of their methods appropriate for such logics. We give some concrete applications as generic examples. Among others, we show that there is a continuum of logics (1) between the intuitionistic predicate logic and the logic of constant domains, (2) between a predicate extension ofS4 andS4 with the Barcan formula. Furthermore, we prove that (3) there is a continuum of predicate logics with equality whose equality-free fragment is just the intuitionistic predicate logic.Dedicated to the memory of the late Professor S. MaeharaThis research was supported in part by Grant-in Aid for Encouragement of Young Scientists No. 06740140, Ministry of Education, Science and Culture, Japan.Presented byHiroakira Ono