### Forcing over models of arithmetic

#### by kamerynwilliams

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 MacDowellâ€“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.

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