# The classification of countable models of set theory

With John Clemens and Samuel Dworetzky. (arχiv)

*Abstract*: We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel complete, meaning that it is as complex as it can conceivably be. We then give partial results concerning the classification of countable well-founded models of ZFC.