On Separating Wholeness Axioms

Abstract

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

17 pages, revised under the reviewer's suggestion