# Scott's problem for models of ZFC

This is my oral exam, which took the form of what was essentially a talk at the CUNY Set Theory Seminar on 31 October 2014.

Scottâ€™s problem asks which Scott sets can be represented as standard systems of models of Peano arithmetic. Knight and Nadel proved in 1982 that every Scott set of cardinality $\le \omega_1$ is the standard system of some model of PA. Little progress has been made since then on the problem. I will present a modification of these results to models of ZFC and show that every Scott set of cardinality $\le \omega_1$ is the standard system of some model of ZFC. This talk will constitute the speakerâ€™s oral exam.