types and thus an interpretation of set theory in expressive type theories. Graph models exist for ZF and also set theories different from Zermelo set theory, such as non-well founded theories. Such models have more intricate edge structure. In graph theory, the graph whose vertices correspond to hereditarily finite sets and edges correspond to set membership is the Rado graph or random graph. See also Hereditary set Hereditarily countable set Hereditary property Rooted trees Constructive set theory Finite set References Set theory