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.