Wednesday, November 20, 20136:30 pmModels of PAGC 4214.03

# When are subsets of a model “coded”?

## Athar Abdul-Quader

### The CUNY Graduate Center

I will present a result by J. Schmerl that characterizes when a collection of subsets of a given model, M, will appear as the coded sets in some elementary end extension of M. This is an analogue to Scott’s theorem, which characterizes when a collection of sets of natural numbers can be the standard system of some model of PA. If there is time, I will also present some extensions of the result.