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.
This is the peer reviewed version of the following article:
Clemens, J.; Coskey, S.; and Dworetzky, S. (2020). The Classification of Countable Models of Set Theory. Mathematical Logic Quarterly, 66(2), 182-189.
which has been published in final form at doi: 10.1002/malq.201900008. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Clemens, John; Coskey, Samuel; and Dworetzky, Samuel. (2020). "The Classification of Countable Models of Set Theory". Mathematical Logic Quarterly, 66(2), 182-189. https://doi.org/10.1002/malq.201900008