A countable Boolean algebra that is Reichenbach's common cause complete

TL;DR

This paper constructs a countable Boolean algebra that satisfies Reichenbach's common cause completeness, addressing a longstanding question about the existence of such small structures.

Contribution

It provides the first explicit example of a countable Boolean algebra that is Reichenbach's common cause complete.

Findings

Established the existence of a countable CCC Boolean algebra

Demonstrated the construction method for such an algebra

Contributed to the philosophical understanding of common cause principles

Abstract

The common cause completeness (CCC) is a philosophical principle that asserts that if we consider two positively correlated events then it evokes a common cause. The principle is due to H. Reichenbach and has been largely studied in Boolean algebras and elsewhere.The results published so far bring about a question whether there is a small (countable) Boolean algebra with CCC. In this note we construct such an example.