Forcing over models of arithmetic
This was a talk at CUNY’s MoPA seminar.
I will talk about forcing over models of arithmetic. Our primary application will be the following theorem, due to Simpson: if a model of PA is countable, then has a subset such that that is a pointwise definable model of PA*. Time permitting, we will see that the MacDowell–Specker theorem fails for uncountable languages: for countable and nonstandard, there are for such that is a model of PA* and has no elementary end extensions.