Model Theory Seminar

In this expository talk I will discuss recent work of Derakhshan and Macintyre on the decidability of the common theory of the rings Z/mZ as m varies through the natural numbers m>1.

I will present a transfer principle in structural Ramsey theory from finite structures to ultraproducts. In joint work with Bartosova, Dzamonja and Scow, we show that under certain mild conditions and assuming CH, when a class of finite structures has finite small Ramsey degrees, the ultraproduct has finite big Ramsey degrees for internal colorings. All Ramsey-theoretic definitions will be provided, and if time permits, I will give a sketch of the proof.