Is Zermelo-Fraenkel Set Theory Inconsistent?

Title: Is Zermelo-Fraenkel Set Theory Inconsistent?

Research Question: The research question of this study is whether Zermelo-Fraenkel set theory, a fundamental system in mathematics, is inconsistent.

Methodology: The author used a logical argument based on the properties of sets and functions to prove a statement. They used Zermelo-Fraenkel set theory as the basis for their proof.

Results: The author presented a puzzle, which is a statement that they proved using Zermelo-Fraenkel set theory. The puzzle states that any algorithm that determines whether a matrix is nonsingular (which can be done in polynomial time) must take at least exponential time in the worst-case scenario. This is a contradiction, as it is known that it is possible to determine whether a matrix is nonsingular in polynomial time.

Implications: The main implication of this research is that the author has presented a puzzle that challenges the consistency of Zermelo-Fraenkel set theory. If the error in the proof can be found, it could potentially lead to a resolution of the long-standing problem of the consistency of Zermelo-Fraenkel set theory.

In conclusion, the research question of this study is whether Zermelo-Fraenkel set theory is inconsistent. The methodology used was a logical argument based on the properties of sets and functions. The main result was a puzzle that presents a contradiction, which challenges the consistency of Zermelo-Fraenkel set theory. The main implication is that if the error in the proof can be found, it could potentially resolve the long-standing problem of the consistency of Zermelo-Fraenkel set theory.

Link to Article: https://arxiv.org/abs/0310060v19 Authors: arXiv ID: 0310060v19