Notes on models of first-order mereological theories

Abstract

This paper will consider some interesting mereological models and, by looking into them carefully, will clarify some important metalogi-cal issues, such as definability, atomicity and decidability. More precisely, this paper will inquire into what kind of subsets can be defined in certain mereological models, what kind of axioms can guarantee that any member is composed of atoms and what kind of axioms are crucial, by regulating the models in a certain way, for an axiomatized mereological theory to be decidable.