Aczel's anti-foundation axiom

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Aczel's anti-foundation axiom is an axiom set forth by Aczel (1988). It states that every finite graph corresponds to one or more sets. In particular, the graph consisting of a single vertex with a loop corresponds to a set which contains itself.

[edit] See also

• Axiom of foundation
• von Neumann universe
• Non-well-founded set theory

[edit] References

• Aczel, Peter (1988), Non-well-founded sets., vol. 14, CSLI Lecture Notes, Stanford, CA: Stanford University, Center for the Study of Language and Information, pp. xx+137, MR0940014, ISBN 0-937073-22-9, <http://standish.stanford.edu/pdf/00000056.pdf> 
• Goertzel, Ben (1994). "Self-Generating Systems", Chaotic Logic: Language, Thought and Reality From the Perspective of Complex Systems Science. Plenum Press. ISBN 978-0306446900. Retrieved on 2007-01-15. 
• Varol Akman, Mujdat Pakkan. "Nonstandard Set Theories and Information Management" (PDF). Retrieved on 2007-01-15.