Abstract

In this paper† we will treat mereology as a theory of some structures that are not axiomatizable in an elementary langauge and we will use a variable rangingover the power set of the universe of the structure). A mereological structure is an ordered pair M = hM,⊑i, where M is a non-empty set and ⊑is a binary relation in M, i.e., ⊑ is a subset of M × M. The relation ⊑ isa relation of being a mereological part . We formulate an axiomatization of mereological structures, different from Tarski’s axiomatization aspresented in [10] . We prove that these axiomatizations are equivalent . Of course, these axiomatizations are definitionally equivalent to thevery first axiomatization of mereology from [5], where the relation of being aproper part ⊏ is a primitive one.Moreover, we will show that Simons’ “Classical Extensional Mereology”from [9] is essentially weaker than Leśniewski’s mereology