On Separating Wholeness Axioms

In this paper, we prove that ${\mathsf{Z}\mathsf{F}\mathsf{C}+\mathsf{W}\mathsf{A}}_{n+1}$ implies the consistency of ${\mathsf{Z}\mathsf{F}\mathsf{C}+\mathsf{W}\mathsf{A}}_n$ for $n\ge 0$. We also prove that ${\mathsf{Z}\mathsf{F}\mathsf{C}+\mathsf{W}\mathsf{A}}_n$ is finitely axiomatizable, and $\mathsf{Z}\mathsf{F}\mathsf{C}+\mathsf{W}\mathsf{A}$ is not finitely axiomatizable.