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

TL;DR

This paper constructs a universal Kripke frame for the variable-free fragment of the reflection calculus RC$^ abla$, providing a detailed algebraic and relational characterization of its semantics.

Contribution

It introduces a novel universal Kripke frame derived from filters on the Ignatiev RC$^ abla$-algebra, linking algebraic and relational semantics for the variable-free fragment.

Findings

Characterization of the set of filters on the Ignatiev RC$^ abla$-algebra

Constructive coordinatewise description of the frame relations

Establishment of a universal Kripke frame for the fragment

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.