The classification of countable models of set theory

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.

References in corpus (2)

• Infinite time decidable equivalence relation theory
• The complexity of classification problems for models of arithmetic

Cited by in corpus (1)

• Equivalence of generics