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This paper will consider some interesting mereological models and, by looking into them carefully, will clarify some important metalogical 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.
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Andrzej Pietruszczak has made a comment on my Claim 1 in his paper entitled “Classical mereology is not elementarily axiomatizable”. His paper is a wonderful exposition of mereological structures and I think his comment is fair. However, the following are some remarks inspired by his comment.
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