Limitation Example We can construct a L which can only hold in an infinite model. Let a=(x)(y)(R(x,y)A∧x≠y→(3z)(R(x,z)∧R(z,y)∧z≠ X∧z≠y) Remark The notion of being finite can not be captured using the machinery of classical first-order logic according to the last Example and TheoremLimitation . Example . . We can construct a L which can only hold in an infinite model. Let α = (∀x)(∀y)(R(x, y) ∧ x ̸= y → (∃z)(R(x, z) ∧ R(z, y) ∧ z ̸= x ∧ z ̸= y)). . Remark . . The notion of being finite can not be captured using the machinery of classical first-order logic according to the last Example and Theorem. Yi Li (Fudan University) Discrete Mathematics June 9, 2013 11 / 15