Craig Alan Feinstein

Title: Craig Alan Feinstein

Research Question: Is Zermelo-Fraenkel set theory consistent?

Methodology: The researcher proposed a puzzle, stating that they could prove that Zermelo-Fraenkel set theory is inconsistent using Zermelo-Fraenkel set theory itself. They provided an example of two matrices and functions that satisfy certain conditions, and claimed that this would prove their statement.

Results: The researcher presented a theorem that they claimed proved their statement. They used induction on m to prove that any algorithm that computes a certain function must compute certain other functions for each matrix that satisfies certain conditions.

Implications: The researcher claimed that their proof showed that Zermelo-Fraenkel set theory is inconsistent. However, they made an error in their proof, as they provided an example showing that their theorem is false. This means that Zermelo-Fraenkel set theory is not inconsistent, as the researcher claimed.

In conclusion, the researcher's puzzle and proposed proof did not show that Zermelo-Fraenkel set theory is inconsistent. Instead, it highlighted a flaw in their proof, which led to a false statement.

Link to Article: https://arxiv.org/abs/0310060v18 Authors: arXiv ID: 0310060v18