This will be a talk for Set Theory in the United Kingdom (STUK 1), to be held in the other place, February 16, 2019.

**Abstract.** We investigate the senses in which set-theoretic forcing can be seen as a computational process on the models of set theory. Given an oracle for the atomic or elementary diagram of a model of set theory $\langle M,\in^M\rangle$, for example, we explain senses in which one may compute $M$-generic filters $G\subset P\in M$ and the corresponding forcing extensions $M[G]$. Meanwhile, no such computational process is functorial, for there must always be isomorphic alternative presentations of the same model of set theory $M$ that lead by the computational process to non-isomorphic forcing extensions $M[G]\not\cong M[G’]$. Indeed, there is no Borel function providing generic filters that is functorial in this sense.

This is joint work with Russell Miller and Kameryn Williams.

Are there any slides for your talk?

No, it was just a chalk talk, based on the (upcoming) paper for notes. I think the paper will be available on the arXiv before long.