Professor Jindrich Zapletal has been awarded an NSF grant titled “Choiceless set theory,” starting May 1, 2024.
The project studies set theory without the axiom of choice. The axiom of choice is known for providing objects which are central to mathematical theory yet are impossible to directly construct, such as ultrafilters on natural numbers. The PI recently developed a method which makes it possible to stratify such objects by intuitive complexity in detail regardless of which field of mathematics they originate. The result of the chart will be an extensive chart of such objects organized by this method. The project involves graduate students.