A note on Reichenbach’s common cause completeness

Abstract

Common cause completeness (CCC) is a philosophical principle that asserts that if we consider two positively correlated events, then it evokes a common cause event. The principle is due to H. Reichenbach and has mostly been studied in Boolean algebras and orthomodular lattices (quantum logics). The results published so far bring about a question of whether there is a small (countable) Boolean algebra with CCC. In this note, we construct such a Boolean algebra. Since finite Boolean algebras can satisfy CCC only trivially, this example is a smallest possible meaningful example.