Zermelo-Fraenkel Set Theory Inconsistency

Title: Zermelo-Fraenkel Set Theory Inconsistency

Research Question: Can Zermelo-Fraenkel set theory be proven to be inconsistent?

Methodology: The researcher used Zermelo-Fraenkel set theory to prove a false statement, which is a common method in mathematical logic to show inconsistency. They defined certain properties and functions, and then used these to construct a proof by induction.

Results: The researcher was able to prove a theorem that, according to their definition, should require at least m steps to determine for an n×n matrix over F2. However, they also provided a counterexample that shows this is not always the case, leading to a contradiction.

Implications: This research suggests that Zermelo-Fraenkel set theory is inconsistent, as it leads to a contradiction. This is a significant finding in the field of mathematical logic, as it challenges a widely accepted theory. It may lead to new research and a reevaluation of the foundational principles of set theory.

In simpler terms: The researcher used a series of logical steps (the theorem and proof) to show that a certain mathematical theory (Zermelo-Fraenkel set theory) should lead to a specific result. However, they also found a situation (the counterexample) where this result is not true, which means the theory is inconsistent. This is a big deal in the world of math, as it challenges a fundamental theory.

Link to Article: https://arxiv.org/abs/0310060v16 Authors: arXiv ID: 0310060v16