Does the universal set operate as the Von Neumann universe in non well founded set theories?

79 Views Asked by At

I've been researching non well founded set theories (E.g. NF, NFU, etc.) and have been wondering if there are any similarities between the universal set & Von Neumann universe ? Or if there the Von Neumann universe exists in some fashion in non well founded set theories. The reason I ask this question is because, from my understanding the Von Neumann universe doesn't deal with sets that 'self refer'. if someone could confirm or correct this for me that would be great.