The Common Knowledge of Formula Exclusion

Abstract

For every set of primitive propositions and agents there is a canonical Kripke structure and a canonical map from any Kripke structure (defined with the same primitive propositions and agents) to this canonical one. A cell of the canonical Kripke structure is a set C such that if any agent considers a point x in C to be possible then all the other points considered possible by this agent are also in C. A cell C has finite fanout if at every point in C every agent considers possible only finitely many other points. We demonstrate a cell of this canonical Kripke structure such that every Kripke structure that maps to this cell does so surjectively, yet this cell does not have finite fanout.