A mathematical analysis of theories of parthood

This paper presents a mathematical analysis of different formal ontological theories of parthood (mereologies). We summarize variants of the theory of General Extensional Mereology (GEM) and compare them with their abstract mathematical counterpart, set theory. In particular, we prove by set theoretical means that there exists a model of GEM where arbitrary summation of entities is not possible. Further, we use Stone’s duality theory for Boolean algebras to classify models of the different mereologies.