It proved that two different systems for set theory that had previously been proposed as foundational were equiconsistent: either both are valid or both lead to contradictions.
They differed from each other in that von Neumann had added to Zermelo's theory a notion of classes, collections of mathematical objects that are defined by some property but do not necessarily form a set.
[1] She and her husband, mathematician Steven Gaal, both moved to Cornell University, beginning as instructors in 1953 but then in 1954 being promoted to assistant professors.
This step was the first time the Cornell mathematics department had offered a tenure-track position to a woman.
[1] In later life, Gaal became a lithographer, making prints that combined mathematical themes with Minnesota scenes.