Godel's Flaw in the Constitution

There are stories about how when Kurt Godel was applying for citizenship he was going to tell the judge about a flaw in the constitution that would allow the United States to become a dictatorship. Einstein told him not to because then the citizenship might not be confirmed. The flaw was never publicly announced and so is the subject of speculation such as in this article, http://io9.gizmodo.com/the-mathematician-who-showed-how-the-us-could-be-made-a-1607024259 . The flaw is the thirteenth amendment.

"The Thirteenth Amendment (Amendment XIII) to the United States Constitution abolished slavery and involuntary servitude, except as punishment for a crime."

The constitution does not define what a crime is. The government defines that. Therefore the government can make a law that causes whatever group they want to be criminals. Those people would be subject to being literal slaves to the government turning the government into a dictatorship over those people. The people would have no legal way to fight back against the government because their right to vote is removed. So no right to vote means the government will not change. 

One could argue this is difficult to implement but Godel being a mathematician would not worry about implementing the solution. He would just worry if the solution was possible. Clearly by making everyone criminals the government would remove their rights to vote and most of the protection of the constitution. That would create a government that could not be voted out.