Aczel's anti-foundation axiom
- Aczel's anti-foundation axiom
Aczel's anti-foundation axiom is an axiom set forth by harvtxt|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.
See also
* Axiom of foundation
* von Neumann universe
* Non-well-founded set theory
References
*citation|id=MR|0940014
authorlink=Peter Aczel|last=Aczel|first= Peter
title=Non-well-founded sets.
series= CSLI Lecture Notes|volume= 14|publisher= Stanford University, Center for the Study of Language and Information|place= Stanford, CA|year= 1988|pages= xx+137| ISBN= 0-937073-22-9
url=http://standish.stanford.edu/pdf/00000056.pdf
*cite book | last=Goertzel | first=Ben | title=Chaotic Logic: Language, Thought and Reality From the Perspective of Complex Systems Science | year=1994 | publisher=Plenum Press | chapter=Self-Generating Systems | chapterurl=http://www.goertzel.org/books/logic/chapter_seven.htm | url=http://www.goertzel.org/books/logic/contents.html | accessdate=2007-01-15 | isbn=978-0306446900
*cite paper | author=Varol Akman, Mujdat Pakkan | title=Nonstandard Set Theories and Information Management | url=http://www.cs.bilkent.edu.tr/~akman/jour-papers/jiis/jiis.pdf | format=PDF | accessdate=2007-01-15
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