A universal Kripke frame for the variable-free fragment of RC$^\nabla$

Abstract

This note characterizes a universal Kripke frame for the variable-free fragment of the reflection calculus with conservativity operators RC$^\nabla$. The frame here is obtained from the set of all filters on the Ignatiev RC$^\nabla$-algebra which is an isomorphic presentation of the Lindenbaum--Tarski algebra of the variable-free fragment of RC$^\nabla$. We give a constructive `coordinatewise' characterization of the set of filters and of the frame relations corresponding to the modalities of the algebra.