Aczel's anti-foundation axiom: Difference between revisions - Wikipedia

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An [[accessible pointed graph]] is a [[directed graph]] with a distinguished [[vertex (graph theory)|vertex]] (the "root") such that for any node in the graph there is at least one [[path (graph theory)|path]] in the directed graph from the root to that node.

The antifoundationanti-foundation axiom postulates that each such directed graph corresponds to the membership structure of a unique set. For example, the directed graph with only one node and an edge from that node to itself corresponds to a set of the form ''x'' = {''x''}. A directed [[cycle graph]] of length 2 corresponds to a set of the form ''x'' = { {''x''} }.

== See also ==