Part 6/7:
The Legacy of Godel and Cohen
The discussions surrounding the Axiom of Choice reached a critical threshold when mathematicians Kurt Godel and Paul Cohen provided groundbreaking findings in the mid-20th century. Godel demonstrated a model where AC holds true, while Cohen showed a model where it does not—a significant revelation that highlights the axiom's flexibly situational nature.
The outcome underscores a vital consideration: rather than debating the absolute validity of the Axiom of Choice, it is pertinent to determine the utility of the axiom concerning specific mathematical frameworks.