A semantical investigation into Leśniewski's axiom of his ontology (Q1078168)

This short paper contains model-theoretic characterizations of Lesniewski's axioms of ontology. It is shown, e.g., that Lesniewski's axiom \(\lambda\) is true in a model if and only if the model is epimorphic to a model called an \(\epsilon\)-structure. The results of the paper are proved by means of standard model-theoretic methods, but they very clearly illuminate the semantic meanings of the axioms in question.